

















































































* c£ * 

O S " « 

" A V -^ V 1 ^ 

• v % *yg%v 4 * > v • 

A <■ •-■• .6 O '- 

• k ’"* **> ,0 ’ V 

>x ^ ‘ J^lL.y^A. n& 


o V 


>°v 



^ O' 



f %, 

-;wv «? * 

<*“ 'O * » * 

jV . ++ ,0^ *^A\ 

J* Str/rtfrA -v C ‘ 

*b r :4m£»- * J 


A (0 


.o~ 



• «* °«. ’?'<c?M3 • 'V - 

1 it- * *Vl\Y'vSr»* ' _, *w/lr‘'* * 0 '’. 

^ '.rrf- y °c> •-:"•’ .o° **> ♦...’ .* 

•••'- > v N .••*. % A *> o ,.■•• 
\ % f /aVv. <•- .«,* »*dSfey» ♦* ^ »., 



• V* 7‘ 

* <C' vO- • 

' ©. . * # *b * < 

> c o^ ’V 




>> 


*i o 





K' ^\. •-SW«* ♦' 

<. *«. » # X> o * < .. < s A 

’ • - .0' c 0 * 9 * '^o £ 

c -W. •-> .-r 


» * » 


-. -o/ :(k 


K >° ** ■• 


$ 'T^ 

v^v K v*^’* / %/*•-.-.» 

* • • ©, <y ,»* 4 % <> v % * ’ * u * c* v0 «* VL% ^ 

'-**• ** A * '^^** V A - ^ ^ 

/ W 7V ■y > ''-? A ^ 

^ ^ -o #k * <A C> +</.*' A <V '••»• A C* 

b ^ *V / °o y ,.^. V c° 

v * w '' - /rx - - *7 A , ^nSNaN ri**t ^ 








A O' 


o_ 





• t 1 




o m A 


* rv -< 4 -, * 

■» r\' & * 



i i 


i %. '-^.’ ^ ■* 

% * ” -» % r 

V :®. v,.« 

k v \ ' LI ■■ hif / Al l B /A AAA1I cn%X . 

V’ w \ • W<v^ %;w/'\;^'<v 



Vs 


« A V ^ 

* $ % 





VV 


o V 


-v.. v^-y . %*• 

*- ^ 0._ «, ,Vw/V.- ->• c, 

' w :BWA\ 

■ Svp_ -^W3^o aV^. 




^° V . 
.,-•’ A o ; ^ 

,<y ,*v'V- 


* W 


•®7 ^7^7 u \‘^\^ v ^ 

> jA ,‘'* t a0 v o • • • * **o ^ • 1 ' # ♦ a 0‘ o °" ° * 

^ a* 'V. « c 


,S vA 


^ *$* 






V, 4 
V* O' 


\>* , s 


by 




0 tj? 

a «y o * 

o alV O * 


+ ,0 "V 


• A v ♦ 

Vv 


* r$» 4y * 

vv 


7 °Y 

* <*> 'V- • 

« ri* _,_ . 

*••* /’ . \ *'••’* ^ 

■0 T c °A -* _ o ^ 


7 . V 


yp. v 



1 r S vA 

r * ^ 'V * 

• ^ 2# ■• . -0. v <1* - ^ _„ . 

<*, '» • »* ,0 o *< ,, >' A 

» • « <$> O ‘ o * » . ’Vi -V t * * . 

* c •Vv^vl < - O A / 

V ^ *' f 

^ <y 




'X 

o V 


y V 


4 O 

*3? <<« 

Cw > ^ <-sy/ib'J4P * ^ * ^hwvvost T n c yyyjKzr * 

tS o *■ % _0 ■* * «l‘ o * > o 

* . i • ,0" V • •. • ’ a* o» * *. i • .cr 

f t o C}* s • • , ^ f • 0 , • • r ^ 






'o .-. •' (y 

V ,o* 15 



\tSi\ "%><? ~d 


V--V V**-*’ < 

•-••- «>. .0 , ’JrL'- *> \> 



.• <5 «J* 

• Jv~ 

** f 0' ■>, '..o’ ^ O 

. j * c - a -> v * ’ cv ,0 

^ ,’itVv ^ .v§fi2v. ^ a % a * 

VV 'WM* ^ V 
• S * V*\ 



.0 » 7 * * * *1 o 

' * r\ A* + ^NhVVvnj * K * 

i rt ; a, * 'XyV 5 ^ • <i( 

‘° %»,♦...• a* 


„■ 

*■"’* 0 f 0 ’ .. _ V ^ > -.To’ ^ ^ * e *^’*’ f°° J .. ^ '* .Vo’ s < 

^ .vafc&. ^ A * v ^ >0 *^ v 




; W 



... * A 

c ^ . I ' * ^ . 

a'I '>rf^-- ^ <-' * 

. "o v . ^ <y 




>°\ . 

x ^* j v 4 - 

* • 1 ' ^ • « 0 -$r 

o .’AL/» > V N . 

• ^ A 

: W 



is^v /% : .fyf: /\ •..,. 

4 <L V . 1 . ■" « v V- « >} « <L 

* fT* «0 O *<,,!* A <’\» ' o • * * ,0 

^ *'■ **b. ^ . k '** ^ ,0* c °_*' * _ ^O 

A * *?<{T/7?^ - rr 



% *•”* * 
• • o. c ,o 

.* tr <** i 

-, s’ j j> ' " \''"V ' 

. A *u aJK*.* v <* 
































































A MANUAL 

* 

OP 


TOPOGRAPHICAL DRAWING. 


«T 

LIEUT. R. S. SMITH, U. S. Army, 

u 

ASSISTANT PROFESSOR OF DRAWING IN THE C. S. MIL. ACAD., WEST POINT, N. T 


SECOND EDITION. 



HEW YORK: 

JOHN WILEY, 535 BROADWAY. 

1804 . 


V 


TA(#\io 

. S(o 


Entered according to Act of Congress in the year 1854, 


BY JOHN WILEY. 

la the Clerk’s office of the District Court of -**e United States for the S< e.hern District 

of New fork. 










V 


TO 

EOBEET W. WE IE, N.A., 

PROFESSOR OF DRAWING 

IN THE 

UNITED STATES MILITARY ACADEMY, 

Mtst faint, N. f., 

THIS MANUAL IS 

MOST RESPECTFULLY INSCRIBED 













































- 





























I pm f n wtad w i l l 








































































PREFACE 


The following pages have been prepared to meet, and in some degree to supply, 
.the demand for practical instruction in Topographical Drawing. The great 
activity which prevails in regard to Internal Improvements, is constantly calling 
into the field numbers of young Engineers; and already many instructive 
works have been addressed to them on almost every detail connected with their 
profession, except map-making. 

The design of this little manual is, to be a practical assistant and office com¬ 
panion, to be consulted on all matters connected with Topographical Drawing, 
from the first sketch of a preliminary survey, to the complete map. Its scope 
is limited to field and office drawing, and nothing else is treated of, but what 
relates to, or is illustrative of, those departments of Topography. 

With regard to the explanatory figures, the greater part of them are auto¬ 
graphic, and, of course, inferior in point of execution to the fine engravings that 
usually accompany such works as this. The author would plead that they are 
intended rather as illustrations of methods than specimens of style; and that 
the student is more familiarly and intelligibly addressed by means of the pen 
and ink, than by the unapproachable perfection of copper-plate. 

The conventional signs everywhere in use, are those here employed and 
explained, but all arbitrary and unnecessary multiplication of them has been 
studiously avoided. ^ 

41 

West Point, 1ST. Y. 

August, 1854. 














CONTENTS. 


■WWWVWA^ 


Introduction, 


Par. 1, 2. 

it 

3,4. 

tt 

5. 

it 

0 . 

n 

7, 8. 

tt 

9. 

a 

10. 

tt 

11. 

tt 

12. 

a 

13. 


Manner of adjusting the margins of a drawing. 

How the lead pencil is to be used in drawing lines. 

Means of facilitating the reduction, enlargement, or copying of 
Maps. 

Indian ink, how prepared for use and tested. 

Qualities of pens and pencils. 

How to draw lines with the rule and by hand. 

Necessity of ruling and constructing all lines and angles drawn. 
Order of parts to be considered in making a drawing. 

Means of avoiding confusion in copying many lines. 
Precautions to be observed in the progress of the drawing. 


Topographical Drawing, 


Par. 

1. 

tt 

2. 

u 

3. 

tt 

4-6. 

u 

7. 

tt 

8. 

tt 

9. 

u 

10. 

tt 

11. 

tt 

12. 

M 

18. 

tt 

14. 


Definitions; classification of objects to be described. 

Of the character of the conventional signs used. 

Two systems of drawing hills—the horizontal and vertical. 

Description of the horizontal system, of the curves of a hill, 
and their projection upon a horizontal plane. 

Distinction between hills and hollows. 

Ground between the curves supposed to slope uniformly. 
Definition of horizontal zone, and mode of its generation. 

Relation between plan and profile, and how the former 
expresses the relative inclination. 

How to find the actual inclination. Scale of inclinations 
constructed and applied. 

Experimental illustration of the formation of horizontal zones 
and their curves, in the pyramid, cone, and hemisphere. 

Method of drawing intermediate curves. Principle on which 
hills are shaded in the horizontal system. 

Practical directions and remarks on the horizontal system. 

How the actual slope of the ground is expressed in the hori¬ 
zontal system. 





CONTENT S. 


viii 

Par. 15. Manner of representing bodies of water in the horizonta 
system. 

“ 16. The vertical system defined. Line of greatest descent—how 

determined. It expresses the true direction of the slope. 

“ 17. How the degree of inclination is to be expressed by the lines 

of greatest descent. Two methods—German or English, 
and French. 

“ 18. German method. Principles of vertical illumination. 

“ 19. Natural limits of the slopes represented. Construction of 

Lehman’s scale of shade for every five degrees of inclina¬ 
tion. 

u 20. Proportions of the black and white in Lehman’s scale expressed 
in arithmetical ratios. 

“ 21. Practical method of expressing these ratios by shading lines. 

“ 22. How to apply the scale to the zones of a hill in shading it. 

“ 23. Rides for finding the ratio of black and white for a given 

slope; and for finding the slope, having the ratio given. 

“ 24. How the scale may be constructed for smaller variations of 

slope. 

“ 25. Necessity of frequently drawing the scale of shade. 

“ 26. French method of using the line of greatest descent. Arith¬ 

metical expression for the degree of declivity. - Limits of 
slopes to be delineated, and of scales suitable for shading 
lines. 

27. First rule, for determining the intervals of the shading lines. 

“ 28. Practical method of applying the first rule. 

“ 29. Method of drawing medial horizontal curves. 

“ 30. Second rule, for determining intervals, and its application. 

“ 31. Application of the rules to the scale of one foot to the mile. 

“ 32. Third ride, for determining the thickness of the shading lines. 

33. Of the length of the shading lines. 

34, 35. Scale of spaces or intervals: its construction and uses. 

36, 37. Tangent movable scale, its construction and application. 

“ 38. Application of principles possible without constructing every 

shading line. 

“ 89. Table of intervals and thickness of lines, &c., corresponding to 

different scales, and method of calculating it. 

40, 41. Remarks on the application of these principles to maps. 

“ 42. Modification of Lehman’s scale of shade by U. S. Coast Survey. 

*' 43. Construction of the scale thus modified. 

u 44. Further modification and simplification of the scale of shade. 

45. hickness of shading line in Lehman’s scale arbitrary. Con¬ 
ditions regulating it. It is determinate in the French 
method. 

46 Scale of shade further roduced, for field sketching. 

** 47. Principles and practice of sketching in the field. Description 

of sketch-book. Examples. 



IX 


CONTENTS. 

Par, 48, 49. Practical remarks on field sketching without the aid of sur¬ 
veying instruments. 

“ 50. Use of the lead pencil in topographic sketching. 

“ 51. How slopes greater than 45° are represented in the horizontal 

# and vertical systems. 

“ 52. Practical instructions in drawing hills according to the ver¬ 

tical system 

“ 53. Conventional signs for representing other topographical fea¬ 

tures. Bodies of water, ponds, streams, <fcc. 

“ 54. Sign for ponds, rivulets, and tides. 

“ 65. Method of representing marshes. 

f< 56. Signs for forest, orchard, and detached trees. 

51-60. Cleared land, cultivated.land, brushwood, and sand. 

“ 61. Signs for building, and other topographical minutiae. Method 

of drawing roads with a right-line pen. „ 

u 62. Proportion between conventional signs and the scale of the 
map. 

“ 63. The use of colors in topographical drawing. 

“ 64. Method of stretching paper to receive colors. 

“ 65. How the outline is to be drawn, and the paper washed. 

u 66. List of colors to be used. Their properties. 

“ 67. How to prepare and lay on a flat tint, what precautions to be 

observed, and how to repair defects, 

“ 68. How to lay on the double or alternate tint. 

“ 69. Application of tints as conventional signs for water, sand, cul¬ 

tivation, cleared land, brushwood, buildings, and roads. 

70, 71. Description of the signs in color for forest and marsh. 

“ 72. When to use the colors without rubbing them as for a flat tint. 

“ 73. Method of representing slopes in a tinted drawing. 

“ 74. Remarks upon the qualities and relative intensity of the tints. 

“ 75. The lightest tints of the map to be laid in first. 

76, 77. Variation in expressing cultivation. Different kinds of in 
closures. 

“ 78. Of lettering a drawing. 1. The proper time. 2. The size 

of the letters—four sizes, and their applications. Table of 
the proportions of the lettering to the scale. Thickness of 
the letters, <fcc. 

“ 79. Practical directions for the study of the formation of letters. 

“ 80. Border, title, meridian, and scales, necessary for a map. 

** 81. Proportions of, and method of drawing the border. 

“ 82. Description of the title, and how to insure its symmetry. 

“ 83. The meridian: necessity of it, and practical method of deter¬ 

mining it on the ground by means of a watch. 

“ 84. Two scales required—one for horizontal distances and one for 

declivities. 

“ 85. Remarks on the conventional signs for topographical mi¬ 

nutiae. 


♦ 


X 


CONTEXTS. 


Of Scales,. 45 

Of the selection of a scale; what scales are convenient, and 
what inconvenient; examj)les of each. The scale for mea¬ 
suring distances ; its construction and use; example. The 
scale for laying off distances; its principles and construe 
tion; examples of the diagonal scale of equal parts for 
decimal ratios. Method of constructing this scale for 
ratios not decimal. Examples of various scales. Capa¬ 
bilities of different scales for expressing features of ground. 
Comparison of decimal and other scales. 

Of Meridians and Parallels of Latitude,.50 

Limits to the use of right lines for meridians and parallels. 
Practical method of drawing meridians and parallels when 
they are projected in right lines, and when they are 
curved, with examples, and tables for converting, in all 
latitudes, a degree of longitude into geographical and 
statute miles. 


Of Projecting Horizontal Curves, from the Motes of 
a Survey,.56 

Slope of the ground between the stations supposed to be uni¬ 
form. Proportion between the horizontal distance and 
the rise or fall to be considered; example. Manner of 
marking out ground for a level survey. Plane of reference 
and reduction of levels. Mechanical method of finding the 
horizontal distances between curves. Description of the 
proportional scale. Application of the scale in the con¬ 
struction of curves from the survey of an area of one 
hundred feet square. 

Of Tracing Curves under Water, by means of Sound¬ 
ings, .59 

Location and projection of lines of soundings. Distribution 
of the soundings, and determination of points of the curves. 
Practical method of distributing soundings over a given 
line. 

Problems connected with Drawing or Copying Maps, . 60 

Prob. 1. To construct a square that shall be a multiple of a given 
square. 

“ 2. To construct a square that shall be equal to <fcc. of a 

given square. 

“ 8. To construct a square that shall be in any proportion to a 

given square. 

e< 4. To construct a rectangle similar to a given rectangle, 



r 






INTRODUCTION. 




1. When a topographical drawing is to be made with the pen, upon Demy or 
Royal paper, select the smooth side of it, and draw the rectangle intended to 
contain the map, in the middle of the sheet. To do this, find the intersection of 
the two diagonals of the paper, by laying a rule from corner to corner, and 
drawing light pencil lines near the middle. This intersection will be the middle 
of the sheet; with which the centre of the drawing must coincide. Draw 
through this central point a line parallel to the lower edge of the sheet, then 
perpendicular to this, and through the same central point, another line. The 
former of these central lines will give the direction of the upper and lower bases 
of the drawing, and the latter that of the upright sides. Lay off, from the 
central point, to the right and left, on the horizontal central line, distances 
equal to half the base of the required rectangle, and through the points thus 
found, dfaw lines parallel to the upright central line: these will be the indefinite 
upright sides. Then through two points on the upright central line, at dis¬ 
tances above and below the centre equal to half the altitude of the required 
rectangle, draw lines parallel to the horizontal central line, and these will com¬ 
plete the rectangle and form its upper and lower bases. 

2. If the drawing is not a square, the longest line of its margin must be laid 

in the direction of the longest edge of the paper. • 

3. When a drawing is to be finished with the pen, it should be always borne 
in mind that the lead-pencil is used only as a guide, or preparation for the pen, 
and that all pencil lines, without exception, must be drawn very lightly , with a 
moderately hard pencil, finely pointed, which being drawn two or three times 
over a line with a very slight pressure, will produce a mark which may be seen 
very distinctly, and be easily rubbed out afterwards. 


v 


INTRODUCTION. 


• • 

Xll 

4. Ruled pencil lines should be drawn a little beyond their exact length, for 
in going over them afterwards with a pen, their intersections can be more readily 
distinguished by means of these projecting ends of the lines. 

5. In copying from a drawing, it is usual, in order to facilitate the getting in 
of the outline, to draw a number of lines of some simple arrangement upon the 
model, and to do the same with the rectangle in which the copy is to be 
made. The easiest method is to divide the drawing into squares, whose sides 
are in directiou parallel to the margin lines respectively, and in length some 
multiple of the shorter side of the drawing, such as ], y 1 ^, or y 1 ^. It is evident, 
however, that any kind or number of lines drawn upon the model will answer 
the same purpose, provided the proposed copy is treated in exactly the same 
manner. Having, then, these similar systems of lines, it will be easy to cause 
the outlines in the copy to pass through squares corresponding to those of the 
model. This process at once suggests the method of enlarging or reducing a 
drawing by increasing or diminishing the sides of the corresponding squares. In 
comparing the proportions of si'hilar drawings, linear measure is always used; 
e. g., a drawing is said to be twice the size of another when it is tw r ice as high 
and twice as wide, though it contains four times the surface. The squares must 
be drawm in pencil, and lightly, as they would disfigure the drawing if they 
could not be entirely removed. 

6. Indian Ink is used in finishing pen drawings. It should be of the best 
quality, which insures its quick and perfect mixture with w^ater, and should be 
rubbed up perfectly black, in a small plate, as pale ink makes the boldest draw¬ 
ings look weak. To test its blackness when mixed, take some in a pen, make 
a pretty broad mark with it upon white drawing paper, and w T ait until it dries, 
when it will display its true strength. After it has become black, it is ready 
for use, and any further mixing w’ill make it viscid. 

7. The steel pens now so generally used are perhaps the best for drawing, 
and tend to produce, by their superior durability, an evenness of style. The 
pen should be not too elastic, nor should it be easily turned from its direction 
by an increase of pressure upon it. Some draftsmen prefer quill pens, which, 
when of a good quality, w T ell made, and frequently renew 7 ed, are certainly unob¬ 
jectionable. 

8. Pencils, as before remarked, should be moderately hard for line drawing 
Faber’s No. 3, or Wolff’s HHH are of the proper hardness. They should be 
pointed by rubbing them on a piece of fine sand paper. (Par. 3.) 

9. In general, all lines drawn by hand (that is, without ruling), are more 


INTRODUCTION. 


Xlll 

easily drawn toivaids the body; and with this view, a topographical drawing 
should he turned on the table in any way that will facilitate that manner of 
drawing. Ruled lines are more conveniently drawn from left to right (always 
along the upper edge of the rule), and for that purpose also the drawing should 
be turned in any direction. But in copying the outlines by the eye, both the 
model and the copy must be placed upright before the draftsman, so that the 
line he is engaged in drawing may be really parallel to the one he is copying. 

10. No line that is meant to he a straight line should be drawn by hana 
Right lines, whether in pen or pencil, must invariably be ruled, no matter how 
short they may be; and if in ink, should be drawn with the right-line pen. Nor 
should a right angle ever be guessed at. All square corners, whatever be the 
shortness of the lines forming them, must be constructed with the proper instru¬ 
ment. Parallel lines also, no matter how short, must be constructed. 

11. In making or copying a drawing, begin with the principal lines in it; for 
example, if a broad stream or an extended sheet of water be represented, begin 
with that; then proceed to the roads, and smaller streams. Prepare everything 
completely in pencil, before taking up the pen to finish; for in doing so, the 
progress of the work is more satisfactory and apparent. 

12. In copying lines which are so close together as that many of them are 
contained in a single square (which is sometimes the case with horizontal curves), 
that square can be subdivided on the model and on the copy, by joining the mid¬ 
dle points of the opposite sides, so that one square will be made into four. Or, 
only alternate curves may be studied and drawn, and the intermediate ones can 
afterwards be easily introduced. 

12. Let the drawing be kept clean. A piece of thin paper should be con¬ 
stantly interposed between its face and the draftsman’s hands. The ink plate 
should be kept on one side, and never in front of the drawing- Preserve the 
paper on which the drawing is in progress from being bruised: it should never 
hang over the edge of the table where the body or arms can press upon and 
break it. 









TOPOGRAPHICAL DRAWING. 


1. Topography is the art of describing the minute features 
of the earth’s surface. Topographical Drawing consists in 
representing, by lines, or some other conventional expressive 
means, the exact shape and figure of the ground in a particu¬ 
lar locality, as well as the dimensions and positions of all 
objects situated upon its surface. Two classes of objects pre¬ 
sent themselves for description ; the one natural , including, 
1st.—mountains, of every extent, their slopes, their rocky sides, 
their gorges and valleys, and in general, every inecpiality in 
the surface of the ground ; 2d.—bodies of water, as the sea, 
rivers, brooks, lakes, ponds, and marshes ; and 3d.—all natural 
productions or conditions of the ground, such as forests, heath, 
meadows, sand, &c. The other class comprises artificial works, 
such as buildings, inclosures, cultivation, roads, &c. Of this 
latter class, buildings may be divided according to their im¬ 
portance, as churches, country-seats, farm houses, &c. In¬ 
closures may be variously represented as ditches, hedges, 
walls, or fences. The different kinds of cultivation need not 
to be discriminated ; but where a distinction is desired, it is 
better to display it* by lettering the ground neatly. Roads, or 
communications, are distinguished as turnpikes, railroads, 
canals, cross-roads, foot-paths, fords, &c. 

2. Every topographical drawing addresses itself to the eye 
as if the spectator were situated above, and looking down 
equally upon every part of it. In representing therefore upon 
such a drawing the relative positions and the dimensions of 
objects, accurate measurements, according to some assumed 
scale, are used, and distances are laid off, as in any other plan- 
drawing. Rut in expressing the nature of objects, many of 

1 



2 


them not being bounded by mathematical or regular fines, 
recourse is bad to certain conventional means, universally 
agreed upon among draftsmen. In some instances, the signs 
thus used are made to resemble, in some degree, the objects 
for which they stand, as in the case of forests, rocks, meadows, 
&c. In others, they are purely conventional, as in the case of 
hills, water, marsh, &c. The pen, the brush, and the pencil, 
by means of lines or colors, offer facilities for topographical 
drawing, which it is proposed to consider in the order in which 
they are mentioned. 

3. The first characteristic to which we naturally direct our 
attention in regard to the topography of a locality, is the 
variation in the surface of the ground, with reference to hill, 
valley, and plain. The two general systems of delineating 
with the pen these important features, will first be noticed. 
These are called, respectively, the horizontal and the vertical 
system. 

4. First. The Horizontal System .—This consists in intersect¬ 
ing the inequalities of the ground by a series of horizontal 
planes, at equal vertical distances apart, and “projecting”upon 
the map the curves in which these planes intersect the surface. 
To explain this process by a familiar illustration, let us suppose 
a hill, rising out of the water, as in Fig. 1 , where such a hill is 
represented in profile —AB being the water-surface. If we 
should walk completely around the base of this hill, exactly 
along its water-mark, we should follow a perfectly level , or 
horizontal curve , for it is formed on the hill side by the horizon¬ 
tal surface of the water. This water line may then be called, 
a curve “ cut out of the hill by a horizontal plane fi and, as 
such, we may measure its dimensions, determine its propor¬ 
tions, and draw, or “project” it on our plan. 

5. Suppose, now, the water to rise one foot. A new curve 
will be defined on the liill-side, in a manner similar to the 
first, and at a vertical distance of one foot above it at every 
point. This new curve will possess properties similar to 
the first one, and may, like it, be determined and projected. 
CD is the plane of the second curve. In the same manner, 
the planes of other curves, at the same vertical distance apart, 
may be conceived, and the curves measured and drawn, as EF 
GIT, IK, and LM. 


9 




3 


6. Let the curves now be projected upon a horizontal plane ; 
that is, suppose the eye to be placed above the hill, so as to 
look directly down upon every point of its surface. The curves 
will then be drawn, as in Fig. 2 (the shading lines excepted). 

7. In this topographical plan, each of the horizontal curves 
gives us, throughout its length, an exact idea of the shape of 
the ground. It we know (as is always known from the other 
parts ot the map) that the inner , or smallest curve, is elevated 
above the others, then we have the representation of a hill. If, 
on the contrary, the outer curve is elevated above all the 
others, then our drawing represents a hollow. 

8. In the spaces between these horizontal curves, or sections, 
we are necessarily left in ignorance of the precise form of the 
ground. But our knowledge will increase with the number 
of curves w T e have ; and if they could be drawn at very small 
vertical distances from each other, or nearly in contact, we 
should have an almost perfect representation of the slope. 
This, however, is neither practicable nor necessary, for when 
w T e have obtained such a number of sections as will furnish a 
knowledge of the ground sufficient for the purposes required 
(and this number may be increased according to the require¬ 
ments of the case), it is allowable, and customary, to consider 
the ground between any two sections as sloping uniformly. • 
The space between any two of these curves is called a horizon¬ 
tal zone. This zone may be considered as generated by a 
straight line, placed in the direction of the slope of the zone, 
and touching both of the curves, and which, being kept nor¬ 
mal* (perpendicular) to the upper one of the pair, is moved 
around the hill, fulfilling constantly the above conditions, until 

it returns to the point whence it set out. The successive posi¬ 
tions of this line are the elements, constituting the surface of 
the zone. 

9. A comparison [Figs. 1 and 2) of the curves with the cor¬ 
responding profile, will show that where the hill is steep, the 
horizontal sections are projected close together, and that 
where the hill is not so steep, they are projected at a 
greater distance from each other; and in proportion to the 


* A normal to a curve is a right line, which is perpendicular to a tangent to 
the curve, at the point of contact. 






4 


proximity or remoteness of the sections, is the steepness or 
gentleness of the declivity. This proportion will always exhibit 
the relative degrees of the slope at any part of the surface. 

10. In order to find the actual inclination of a zone at any 
place, find the element at that place by drawing a normal to 
the upper curve of the zone. Construct, with the normal line 
m n [Fig. 2) so found, as a base, and with the known vertical 
distance between the sections as an upright, a right angled 
triangle; its hypotlienuse will be equal to the true line of the 
slope, and the acute angle at the base will be equal to the angle 
of inclination required. 

This triangle is seen at AC& [Fig. 1), and the angle CAa 
is the angle of inclination. Or construct, for all cases, a scale 
of inclinations, as follows:—Draw the lines AO and OB [Fig. 
3), forming a right angle at O. Lay off with a protractor, the 
lines O 5, O 10, O 15, O 20, Ac., making, with OB, angles of 
5°, 10°, 15°, 20°, Ac., successively up to 45°. To use this 
scale, draw the line CD parallel to OB, and at a distance above 
it equal, according to the scale of the map, to the vertical dis¬ 
tance between the horizontal sections. Having, as aforesaid, 
found the normal at any point, take its length in the dividers 
(or compasses), set one foot of the dividers at C, and the other 
towards D, on the line CD, and observe its position with re¬ 
gard to the intersections of CD with any of the lines O 5, O 10, 
Ac. For example, should the length of the normal be Ce, the 
inclination is 5° ; should it be Cy, it is 10° ; should its extre¬ 
mity fall at f, midway between e and y, the inclination is 7£°. 
If it fall at a point not easily determined as to its position, 
draw a line from O through it, and measure, with a protractor, 
the angle formed with OB. This scale may be made more 
exact, by laying off angles of less than 5°. 

11. To show how these horizontal sections contribute to the 
knowledge of forms, Figs. 4, 5, and 6, are plans and profiles of 
the pyramid, cone, and hemisphere. The upper portion of 
Fig. 4 is an elevation —that is, a vertical view, or “ projection” 
of a square, right pyramid. It exhibits the vertical dimen¬ 
sions. Suppose this pyramid to be three inches in height, and 
to be made of wood, or some soft material. Drill a fine hole 
from the apex to the middle of the base; it will pass through 
the central line, or axis, of the figure, and will be perpendicu- 


4 


5 


lar to the base. Suppose, now, that w T e saw or cut the pyra 
mid into six slices, \ inch thick each, by passing the saw 
parallel to the base at each cut. Set up the pyramid again, 
pass a stiff wire or needle through the drilled axis, and place 
it upon a sheet of paper on a horizontal table, so that one of 
the lines forming the base shall be parallel to, or coincident 
with, a right line drawn on the paper. Press the wire-axis, so 
as to mark the centre of the base, and draw a pencil line 
around the base of the body. This will be the lower outline of 
the undermost zone. Pemove now, the lowest slice, and let 
the next one above come down upon the paper, keeping the 
axis in the same place, and the sides of the base in the same 
direction as before. Draw a line around this new base with a 
pencil, and it will give the upper outline of the undermost 
zone, or, which is the same thing, the lower outline of the 
zone next to the lowest one. By repeating this operation in 
the same way, we shall obtain the upper and lower outlines of 
all the six zones of the figure. The upper outline of the upper 
zone is the apex, and wfill be represented by one point, in the 
middle of the base. The sections of such a pyramid will 
thus be found to be a series of concentric squares, whose ver¬ 
tical distance from each other is the assumed thickness of the 
slices into which it has been divided, and whose horizontal dis¬ 
tance apart is the base of a right-angled triangle, whose per¬ 
pendicular and hypothenuse are respectively the vertical 
thickness of the zone, and the length of the normal, or true 
slope of the zone. (See Fig. 4, at b.) 

The same method of demonstration, and the same remarks, 
will apply to the cases of the cone and hemisphere; and an 
examination of the figures (5 and 6) will show the manner of 
drawing, and connecting the vertical and horizontal projections 
(or the elevations and plans) of those bodies, when treated in 
the same way as the pyramid we have been considering. 

The sections of the cone (a right cone with circular base) 
and of the hemisphere are concentric circles. In the case of 
the cone they are equidistant, and their horizontal distance is 
fotind as in the pyramid. This equidistance of the sections 
indicates a uniform declivity. In the hemisphere the upper 
sections are more removed from each other than the lower, and 
the horizontal distance between them diminishes rapidly as we 


6 


approach the lower ones, which indicates an increase in the 
declivity [Fig. 6). The eye should be familiarized with this 
kind of projection, so that a distinct idea of the form of any 
object may be received or conveyed by means of sections cut 
out by equidistant horizontal planes. 

12. We have thus far considered a hill as given only by such 
a number of sections as could, or needed to be accurately de¬ 
termined by survey or otherwise, assuming the slope between 
these determinate sections to be uniform. But we can now 
fill up this skeleton plan, and draw any desired number of 
curves in each zone, by dividing and sub-dividing the normals 
by medial sections. If we draw through the middle points of 
the normals of any zone a medial line, we shall have (by the 
principle— Par. 11—that equidistant sections indicate uniform 
slopes) a new curve cut out of the surface by a medial hori¬ 
zontal plane. Dividing medially these secondary zones, we 
shall obtain two more auxiliary curves, and so on for any 
number. 

It is upon this principle that drawings are filled up or shaded, 
in the horizontal system. When we have determined and pro¬ 
jected a sufficient number of curves, so that the assumed uni¬ 
formity of slope between them does not differ essentially from 
the truth, we can proceed to fill in, without constructing them, 
as many curves as it may be desirable to have in the spaces 
between the determinate ones. And if we keep always the 
same number of shading lines within each pair of curves, they 
will, by their proximity or remoteness, as the width of the zone 
diminishes or increases, serve to show the relative steepness of 
the slope. The darker shade produced by their drawing closer 
together, and the lighter color caused by their separation, will 
contribute to the same effect. And it is from this (in con¬ 
nexion with vertical illumination, which will be referred to in 
explaining the vertical system) that has been derived the con¬ 
ventional idea that a dark color represents a steep slope, a 
lighter color a more gentle one, and perfect white a level. See 
Fig. 7 for an example of this method of finishing hills. 

13. Practical Directions and Remarks on Drawing a IIili 

ACCORDING TO THE HORIZONTAL SYSTEM. 

Having prepared the outlines of the drawing in light pencil 
lines, including the skeleton curves of all the hills or hollows, 



7 


proceed to finish with the pen and ink. In commencing the 
shading lines, place the drawing on the table so that the sum¬ 
mit of the hill shall be towards the left hand (see Fig. 2). Then 
draw (towards the body) as many lines within the highest pair 
of curves (say six, more or less, according to the large or small 
scale of the map), as you intend to put in each horizontal zone. 
Thus, if the determinate curves are constructed at a vertical 
distance of one foot apart, our auxiliary ones will be about two 
inches apart vertically. If the scale is smaller, and the deter¬ 
minate curves are drawn six feet apart, our shading lines will 
have a vertical distance of about one foot. Draw the lines 
with firmness, and let them have a length varying from about 
£■ of an inch to about 3 of an inch, according to the width of 
the zone, that is, according to the greater or less degree of 
declivity (Fig. 2, at o and jp). Where the hill is steep, the 
lines are heavy and short; where it is less steep, they are 
longer and lighter, and in approximating the level they 
must be drawn as fine and clean as possible. Let them divide 
equally the space between the curves. Go all around the 
hill in this manner, in each zone, before commencing the 
one next below it, turning the drawing on the table so as to 
draw always towards the body, increasing or diminishing the 
distance between the lines as the width of the zone varies, so 
that they just fill the zone evenly; and finish by joining them 
together where they began. Proceed in like manner with the 
second zone, and so on to the bottom of the hill. Inasmuch 
as we have the form of the hill accurately defined in pencil by 
the skeleton of curves, it is not absolutely necessary that, in 
shading, the accessory curves should be rigorously continuous. 
A slight variation in their position at the joints, provided they 
do not wander out of their zone, imparts a degree of freeness 
to the style. Be careful to connect the sets of lines together, 
end to end, so that the groups shall not be separated by a va¬ 
cant space (Fig. 2, at ?•), or be overlapped by thrusting the lines 
of one group between those of another (Fig. 2, at s). Endeavor 
to obtain a clear, even tint. Do not let the junctions of the 
groups in the different zones form continuous lines down the 
hill (Fig. 2, d , d), but let them “break joints,” by frequently 
bringing a junction opposite to the middle of the group in the 
zone above (Fig. 2, at e , e , e). 


* 


8 


14. When a drawing of a hill is finished according to this 
system, and the pencil lines removed, the zones formed by the 
determinate curves are no longer distinguishable, and the 
means of ascertaining actual heights and inclinations are lost. 
This difficulty may be obviated either by marking the deter¬ 
minate curves by light lines of red, and numbering them ac¬ 
cording to their vertical distance above or below a certain 
assumed level, and from each other; or by writing upon the 
map a statement of the vertical thickness of a zone, and how 
many auxiliary sections are contained in it. 

15. Whenever this horizontal system is used in representing 
slopes, the conventional sign for bodies of water consists only 
of a narrow strip of tint, or shade, produced by short lines 
drawn parallel to the base of the drawing. Draw these lines 
towards the body, and from the shore outwards, having first 
defined the width of the strip by means of a fine pencil line 
{Fig. 7 at A). 

1G. The other method of representing hills, which is called 
the Yeutical System, is now to be considered. It consists in 
expressing the inclination of a hill-side, by drawing its lines of 
greatest descent. The two required elements are both to be 
exhibited in these lines, viz. the direction and degree of the 
slope. The direction of any line of greatest descent (which is 
the true direction of the slope or inclination), is obtained by 
considering the horizontal sections of the surface. Let us sup¬ 
pose a hill {Fig. 2) given by its curves. If, from the summit of 
this hill, we suppose water to flow, or a round mass or body 
to be rolled, it will evidently, under the influence of gravita¬ 
tion, seek the lowest point, and that by the shortest line. This 
path, so described, will be the “ line of greatest descent .” It is 
further to be observed, that this line will be found constantly 
perpendicular (normal) to the horizontal sections. For any de¬ 
viation from this direction {Fig. 2, f g) displays a spiral ten¬ 
dency, or a tendency to move around the hill, which cannot be 
imparted by gravitation* Having then the horizontal sections 
given, we can always draw, perpendicular to them, any num- 


* Any deviation from a direction perpendicular to the horizontal lines is an 
approximation towards a line of no descent, and in so far, a departure from a 
line of greatest descent. 




t 




9 


her of lines of greatest descent, thereby obtaining a complete 
knowledge of the direction in which the ground slopes (Fig. 15). 

17. The other, equally important, element of the inclination, 
viz. its degree of declivity, is expressed by means entirely con¬ 
ventional. Two methods have been adopted for this purpose : 
one depending upon the principle of vertical illumination, in 
which the maximum light is reflected upwards to the eye by a 
horizontal surface, and a minimum by a surface inclined 45° to 
the horizon. The latter, being the steepest slope at which earth 
will stand, is taken as the limit of least illumination. This is 
the English and German convention, and lays more stress on 
the different proportions of black to white in indicating the 
degree of slope, than upon the distances between the shading 
lines. The other method (the French) makes its expression 
depend more upon the distance between the lines of greatest 
descent than upon the color produced, although in it also, the 
tint is graduated from dark to light, or white, according to the 
declivitv or level to be shown. These two methods of deline- 
ating hills will be considered in the order in which they are 
named above. 

18. When the surface of the ground is illuminated by verti¬ 
cal rays, it is evident that the level or horizontal part's will 
reflect upwards to the eye (which is supposed to be situated 
vertically above every point of the map) the greatest quantity 
of light, for the incident rays then coincide in direction with 
the reflected ones, the rays of light being supposed to be paral¬ 
lel. But when a vertical ray falls upon a surface inclined 45°, 
the reflected ray will be horizontal, since both rays make 
angles of 45° with the line drawn perpendicular to the surface 
(Fig. 8). 

19. The natural limits of the declivity of slopes being 45° for 
the greatest, and a dead level for the least, it is required to 
apportion the illumination between these limits, taking black 
to represent a slope of 45°, and white a horizontal plane. Di¬ 
vide the line A B (Fig. 9) into ten equal parts, corresponding to 
the ten steps of a gradation (by 5° at a step), from a level to 
a slope of 45°. Upon the line C D, below, represent in these 
divisions, the different inclinations, viz. a level, 5° slope, a 
10°, 15°, &c., to 45°. The level is perfectly white. Then there 
are nine degrees of color to' be determined, from 5% which is 


# 


the lightest shade, to 45°, which is black. Divide now each 
of the ten spaces of A B into nine equal parts. To exhibit the 
proportion of black to white in a slope of 5°, make one of those 
parts black; for 10°, make two black ; three for 15°, and so 
on to 45°, where all nine parts are black. 

20. This scale of color shows the following proportions of 
black to white for all the inclinations (differing by 5°) from a 
level to a slope of 45°. All the nine parts of the part of the 
scale corresponding to the level are white. In a 5° slope, 
one part of the nine is black, shcAving a proportion of black 

to white as 1 is to 8. In 10° two parts out of the nine are 

black, showing a proportion of 2 : 7, or 1 : Si. For 15° the 
proportion is 3 : 6, or 1 : 2. For 20°, 4 : 5, or 1 : H. For 

25°, 5 : 4, or 1£ : 1. For 30°, 6 : 3, or 2 : 1. For 35°, 7 : 2, 

or 3^ : 1. For 40°, 8:1. For 45°, all is black. Expressing 
these proportions in the form of ratios, we shall have the fol¬ 
lowing table, in which the numerator signifies the quantity of 


black, and the 

denominator the quantity of white :— 

Level. 

No. 

Black. 


5° 

1 

5 

a 


10° 

2. 

7 

a 


15° 

2 

e 

a 


20° 

4 

5 

a 


25° 


a 

or 1 more black than white. 

30° 

6 

3 

a 

or i “ “ 

35° 

@ 

1 

2 

it 

or 31 “ “ 

40° 

8 

1 

it 

or 8 “ “ 

45° 

all 

it 



21. To reduce these ratios to practice in the drawing of shad¬ 
ing lines, the four horizontal strips, below the lines E F, G H, 
I K, and L M (Fig. 9), show how the black portion of each 
set of nine parts is divided up into lines of proper thickness 
for use. For example, in the strip E G of the rectangle 
orsp which corresponds to the slope of 5°, the 1 black part 
to 8 of white, or 1 to 8, is divided into two black lines of half the 
thickness of the first black part, showing a proportion of 2 : 16. 
Each of these lines is, in the strip G I, divided into two of half 
the thickness of those in E G, making four shading lines, show* 
ing a proportion of 4 : 32. Dividing these in the same manner 


11 


we obtain, in the strip I L, a proportion of 8 : 64, and in tbe 
next strip below, of 16 : 128. (See Par. 45.) 

22. It remains to sliow the use of this scale, in expressing, 
by the ratio of black to white, the degree of inclination of a 
slope. For this purpose the scale must be cut otf along the 
line L M. The part LCDM will then furnish us, along the 
line L M, with a graduated edge, by means of which the dis¬ 
tance between the centres of the shading lines can be marked 
off, and the line C D will show the different slopes to which 
the graduation corresponds. 

Having now the horizontal sections of a hill given, write 
upon it with a pencil, in as many places as necessary, the degree 
of the inclination (See Par. 10), and bring the line L M of the 
scale tangent to the upper curve of the zone, at that part of 
the scale corresponding to the inclination we are required to 
express, and mark off from its edge the distances between the 
centres of the shading lines. Through each of the points thus 
determined draw a line of greatest descent (See Par. 16). Copy 
from the scale, for each group of the lines, the exact proportion 
of black to white, and the color in each zone will then express 
the degree of the slope, and the line of greatest descent will 
show its direction. 

23. From the foregoing we deduce the following two practi¬ 
cal rules. To find the ratio of black to white for any given 
slope: Pule 1. Subtract the given inclination from 45° for a 
denominator , and take the given inclination for a numerator , 
and we shall have the ratio as in the table in Par. 20. Apply 
this, for example, to the expression of a 20° slope. Take 45°—• 
20° = 25 for a denominator. The numerator is 20, hence §£, 
or | is the ratio (see Par. 20), of which the numerator repre¬ 
sents the black. To find the inclination, the ratio of the black 
and white being given, or having been observed from a draw¬ 
ing : Pule 2. Multiply the numerator of the given ratio by 
45 ° for a new numerator , and add together its numerator and 
denominator for a new denominator. Reduce the fraction. 
For example, in reading a drawing, we find in a certain part 
a ratio of black and white expressed by the fraction f. Then 

° X -~- — — 25 —the inclination required. 

5 + 4 9 

24. In the above calculations, as well as in the scale of shade, 


r 




12 


no variations of less than 5° have been regarded; but smaller 
differences may be used, if desirable, and the scale drawn, and 
the ratios calculated in the same manner. 

25. In representing declivities by this method, considerable 
practice is required. This should be commenced by drawing 
repeatedly the scale of shade, particularly the last subdivisions 
of the black part into lines, so as to apportion accurately the 
black line to its adjoining white spaces, in such a manner as to 
express with readiness any of the angles of inclination into 
which the scale is divided. Then the line may be applied to 
express the varying inclinations of the same, or of different 
zones of a hill. 

It is not, however, to be supposed possible that every angle 
can be expressed in the exact proportions of the table of ratios. 
The most experienced eye and hand are liable to deviate about 
2° from the truth, in estimating angles less than 9° and greater 
than 34°, and about 1° in estimating the intermediate angles. 
But it is seldom necessary to approach nearer than this to the 
truth. 

26. The other method (the French) of expressing convention¬ 
ally the degree of inclination, by means of the distances be¬ 
tween the centres of the lines of greatest descent, will now be 
considered. In discussing this system, slopes are expressed by 
a written fraction, the numerator of which is unity, and gene¬ 
rally stands for the vertical distance between the horizontal 
sections, and the denominator is the horizontal distance between 
them (or the normal, see Par . 10), expressed in terms of the 
vertical distance as a unit. For example, let a b {Fig. 10) be 
the profile of a slope, cut by horizontal planes at a and b; call 
be 1 (unity), and designate the line a c by s. Then the slope 
will be represented by J-. If b c is contained three times in 
a c , then the expression for the slope will be £, and so for 
any other relation between the base and perpendicular of the 
right-angled triangle a b c. The limits between which slopes 
are represented in this method, are -f or 45° for the greatest 
and eV, or 0° 53' 43" for the least—all slopes less than the 
latter being regarded as levels. The largest scale that will 
admit of conveniently drawing the lines of greatest descent, is 
elo of the full size, or 6 inches to 100 yards, being about 8f 
feet to a mile. In drawings made to this, and smaller scales, 



13 


tlie vertical distance between the horizontal sections is sene* 

O 

rally taken one yard. For the scale of we shall hare, as 
the least width of zone, T | T of an inch, and for the greatest, 

6 84 . , 

-X 64 ~ 3-inches 

100 100 eb * 


To fill a zone wider, or even as wide as this, with lines of 
descent, would be inconvenient, and unnecessary. 

27. In order to determine the interval between the shading 
lines for any given inclination (which interval is always rec¬ 
koned from centre to centre of the lines), we have the follow¬ 
ing rules :— 

Rule 1. To the distance (measured along the line of greatest 
descent) between the upper and lower curves of any zone , add 
three-tenths of an inch ‘ a sixteenth part of this sum will be the 
proper interval for the shading lines. For example, if the 
given inclination is the scale being ¥ 1^, and the zones 1 
yard thick, the width of zone for will be .06 x 60 = 3.60, or 
3 t 6 0 inches; to this add T 3 F of an inch, and divide by 16, and 
we have 


3.60-b .3 3.9 
~~"16 = Iff 


0.244. 


If the inclination is |, we have 


.06 + . 3 .36 . , 

--—= —=0.0225 inches, <fcc. 

lo lo 


28. To save the labor of calculation, the following is a prac¬ 
tical method of laying off these points by the eye. Cut a rec¬ 
tangle of paper, the side A B, of which (see Fig. 11) must be 
ecpial to T \ of an inch. It is required to space off the shading 
lines at MH, which is a line of greatest descent. Apply the 
rectangle near the middle of MH, with the side AB laid in 
the direction of the middle of the zone, and towards the left. 
Prolong AB to the right, and make BE equal to MH. Then 
AE will be equal to the width MU of the zone, plus 3 3 ff of an 
inch—which distance is to be divided into 16 parts. How, by 
the eye (or with compasses, until the eye is sufficiently prac¬ 
tised), halve the line AE at o, quarter it at p and r , treat the 
quarters Ap , po, or , and rE\ in the same manner, and through 
each of the 17 points so found, a shading line is to be drawn 
across the zone. 




14 


29. When the curves are nearly parallel, we can easily in this 
manner, determine seventeen lines at once. But when the curves 
depart from each other rapidly, the lines of greatest descent 
also diverge proportionally, and a right line drawn normal to 
the upper curve, as at G {Fig- 11), will have departed from 
the path of greatest descent GI, when it reaches the lower 
curve at II. It therefore becomes necessary to correct its 
direction. This is done by dividing the line of greatest descent 
into four or more parts, and thus determining three or more 
medial sections (see Par. 12). The true line of slope GI {Fig. 
11) is thus divided, and by similarly dividing others, as at 
YZ, &c., we can draw the auxiliary sections ab , cd , and ef. 
These sections being approximative! y parallel, we are now pre¬ 
pared for the application of 

30. Pule 2. To a quarter of the distance (measured as before) 
betwee7i the upper and lower curves of any zone , add „ of an 
inch • a fourth part of the sum will be equal to four intervals. 

Cut a rectangle of paper as before, whose side A'B' shall be 
o °f an inch. Apply A'B' to the middle point of the nor¬ 
mal drawn at F {Fig. 11). Make B'P equal to FIv, and divide 
A'P into four parts, by halving and quartering as before. 
This will determine 5 lines, to be drawn as far as the auxiliary 
section ab. Apply A'B' to the left of the second normal IvL, 
and determine four lines of the second auxiliary zone, and so 
on for LO and OQ. 

31. These rules have for example’s sake, been now applied 
to a drawing made on a scale of 6 £ 7 . Let it be supposed that 
the scale is or 1 foot to 1 mile. In this scale it is suffi¬ 
cient to consider the curves as being 2 yards apart vertically. 
Then the least width of zone will be 0.0136 inches nearly, 
which is very small, while the greatest width will be 0.8704 
inches. Now, for a slope of { or 45°, the 1st Buie will give for 
the intervals 


.0136+ .3 .3136 

To ~~1F = 


0.0196, 


or T |o of an inch, nearly; and for a slope of we shall have 


.8V + .3 
16 


.90 

— = 0.05625, 
lb 


or 51 hundredths of an inch. This is a small scale, and is 




15 


adapted to exhibit a portion of tlie ground from four to eight 
miles square. 

32. Having now established the intervals of the shading 
lines, it remains to regulate their thickness, or breadth, so as to 
assist in expressing the declivity. For this purpose, they will 
vary directly as the inclination, agreeably to the following 

Rule 3. j For a slope of f, the thickness of the shading lines 
is equal to two-thirds of the distance between their centres , and 
their thickness will diminish with the inclination , down to A) 
where the lines will be as fine as they can be drawn. This rule 
will always, in a slope of }, make the shading lines twice the 
breadth of the white space contained between them {Fig. 12). 
Thus, for a scale of F the zone being 3 feet in height, and the 
slope }, we shall have for the intervals 


.06-f-.3 .36 

16 ~~16 


two-thirds of which, 


or 

.36x2 .72 

16X3~ 48~’° 15 ’ 


or 1| hundredths of an inch, nearly. If the scale is j 2 V 05 the 
zone being six feet high, we shall have the intervals for a slope 
of 1 , 

.0136-{-.3 .3136 

16 “ 16 ' 


two-thirds of which 

.3136X2 .6272 

~16~x3~ ~ 


.0131, 



or nearly 1 h hundredths of an inch as before; in both these 
(and all other) instances, the shading lines decreasing to the 
finest line, to express the slope of 

33. In regard to the length of the shading lines, no absolute 
rule needs to be laid down. As there is no contemplated rela¬ 
tion between the declivity and the length of the shading line, 
this part of the work is left to the skill and discretion of the 
draftsman. It may be remarked however, that if we confine 
their length to the width of the zone, their thickness, in a slope 
of }, would sometimes exceed their length; and in a slope of 
t hey would often be too long for convenience. In the latter case, 
this difficulty is obviated by dividing the zone {Par. 29); and 







16 








in the former, it may be observed, that the lines may be drawn 
across 4 or 6 zones, more or less, according to the scale, and 
other circumstances. The extremes of length for ordinary 
scales, may be set down at I or } of an inch for the steepest 
slopes, and about 4 of an inch for the gentlest. Some further 
practical directions will be given on this subject hereafter. 

34. Upon every drawing made in accordance with the above 
rules, there should be placed a scale, which should conve¬ 
niently shew the relation between the width of the spaces and 
the slope of the ground at any part of the map. 

The following is a convenient form for this scale:—Divide a 
line AB {Fig. 13) into 64 equal parts, by setting otf from A 
towards B, 64 spaces of (say) T V of an inch. Number the divi¬ 
sions from A to B, calling the point A zero, and B 64. Let 
fall perpendiculars from A and B. On that at A, measure 
downwards to &, a distance equal to the width of four spaces 
corresponding to a slope of }, and at B measure downwards to 
£>, a distance equal to four spaces, expressing a slope of 
Join a and b by a right line. Let fall now, perpendiculars 
from every point of division on AB, until they intersect the 
line ah , and the scale is completed. 

To make use of it in finding the declivity expressed by the 
shading lines, take off in the dividers, the width of four spaces 
at any part of the drawing, and compare it with the lengths of 
the perpendiculars to A B. If, for example, it is found that it 
coincides in length with No. 12 of the scale, then the slope 
expressed by that interval is T \. 

35. Reciprocally, this scale may be used to determine the 
width of four spaces. For, having constructed it, as before, in 
the same scale of distances as the map to be drawn, and know¬ 
ing as we do, the expression for the slope at any part of the 
drawing, the perpendicular of this scale of intervals, which 
agrees by its numeration on A B with the denominator of the 
slope-ratio, will evidently be the corresponding width for four 
spaces at that place. 

36. A still more convenient practical method of marking off 
the intervals, and drawing the shading lines of the proper 
thickness, consists in the use of a tangent movable scale, to be 
applied along the horizontal curves. It shows the relation 
between the length, thickness, and the intervals of the shading 


IT 


lines for nil slopes. Its construction and use are as follows :— 
Draw a right line A B {Fig. 14). At A, draw perpendicular to 
it, and downwards, a right line, whose thickness and length 
shall both correspond to a slope of \. This line must be 
drawn according to the scale of the map. Bor example, if the 
scale of the map is or 1 foot to 400 yards, the horizontal 
curves being 3 feet apart vertically, or T f 7 of an inch, accord¬ 
ing to the scale ; then (Far. 26) the width of zone for a slope 
of |, is .03 inches. The length of the shading line will then be 
.03, and its thickness (by Buie 3) is .0137 inches. Having 
drawn this line, of the proper length and thickness, lay off 
towards B, the first interval of the scale, which must corres¬ 
pond to a slope of {. By Buie 1 (Far. 27), we have 


.03 + .3 
16 


.33 

— =3.0206 


for this interval, and for w r e have .1387. How, from -f, 
the slope expressed by the former distance, the intervals go on 
increasing uniformly up to A? which is expressed by .1387. 
They may, therefore, be regarded as an arithmetical series, 
whose first and last terms are .0206 and .1387, respectively, 
and whose common difference is 


.1387 —.0206 
--—=.001875. 

By adding this common difference 64 times to the first inter¬ 
val (.0206), we shall, by laying them off from A, obtain the 
successive intervals of the scale. When the scale is very 
small, the common difference may be doubled, and the inter¬ 
vals laid off from A, by two at a time, and afterwards halved; 
or it may be quadrupled, and four spaces laid off at once, and 
then divided into four equal parts. Under such circumstances, 
these will approximate, very nearly, the true division. 

This, by successive additions, is the most accurate method 
of setting off small distances. Let fall, now, through these 
points thus determined on the line AB, perpendiculars to AB, 
of indefinite length, and varying uniformly in thickness, from 
the first line at A, which is .0137 of an inch thick, to the last 
one at B, which is as fine as possible. To determine the 
lengths of these shading lines, or in other words, the width of 
the zone to which their intervals and thickness correspond, 

2 




18 


start from the first line, already drawn of the proper length 
( T f o in.) at A , and from that line increase the length of each 
one, up to the 64th, in an arithmetical progression, whose first 
term is .03 the least width of zone, and the last 1.92 the greatest 
width. The common difference of this series is .03, and by 
successive additions (as in spacing off A B), the increasing 
lengths of the perpendiculars may be laid off. Having done 
this, draw through their lower extremities the curve D C, 
and the tangent scale will be completed. Each division of the 
line A B is the interval between two shading lines, correspond¬ 
ing to a width of zone equal to the mean of the two perpendi¬ 
culars which include it. 

37. To make use of this scale it must be cut out, following 
its outline, A B C D A. Place the line A B on the draw¬ 
ing, tangent to one of the horizontal curves, so that the perpen¬ 
diculars to A B shall be normal to the curve, and coincide in 
their length with the width of the zone. Let the lower curve 
of the zone cut the curved outline C D, midway between two 
of the perpendiculars. See Fig. 14, at m n and o p, where the 
adjustment of the scale at m n gives the interval and thickness 
of the shading lines by means of the perpendiculars, m o and 
up, which are in length and direction the normals of the zone 
ef ’, g A, at m and n. This scale may thus be applied to deter¬ 
mine groups of lines in different parts of the hill. 

38. Although the representation of the ground is thus con¬ 
formed to geometrical rules at all points, it must not be thought 
necessary to repeat the process of construction for every line. 
It will suffice to do so at those places where the slope exhibits 
the greatest variations. Thus, a group in each zone will be con¬ 
structed where the slope is least, and again where it is greatest, 
then a few intermediate ones. By graduating the changes in 
the shading lines, in passing from group to group, both as to 
their thickness and their intervals, we can easily fill the va¬ 
cancies between the determinate groups. Without being ma¬ 
thematically exact, we shall thus obtain a result sufficient for 
all practical purposes, and as accurate as can reasonably be 
looked for in employing the lines of greatest descent. 

39. Tabular view of the width of zone, the intervals and 
thickness of the shading lines, corresponding to different scales, 
and different heights of zone:— 


19 


Scale. 


i 

600 

1 

600 

l 

1200 

1 

1200 


5260 

1 

loSiO 

1 

15640 

1 

80000 


Height of zone. 

i 

Least width of 

zone according 

to the scale. 

Greatest width 
of zone. 

Greatest inter¬ 

val of shading 
lines. 

Least interval 

of shad’g lines. 

Thickness of 

lines for 45 u . 


1 foot. 

.02 

1.28 

.09875 

.02 

.01333 

1 in. to 50 ft. 

3 feet. 

.06 

3.84 

.25875 

.0225 

.015 

ii it 

3 feet. 

.03 

1.92 

.13875 

.0206 

.0137 

1 in. to 100 ft. 

6 feet. 

.06 

3.84 

.25875 

.0225 

.015 

ti ii 

6 feet. 

.0136 

.8723 

.07327 

.0196 

.0131 

12 in. to 1 mile. 

11 feet. 

.0083 

.5212 

.0513 

.0192 

.0128 

4 in. to 1 mile. 

22 feet. 

.0166 

1.062 

.0851 

.0198 

.0132 

ii ii 

60 feet. 

.00075 

.048 

.02175 

.0188 

.0125 

n’ly 8 in. to 1 m. 


To calculate the values of the above different quantities, first 
find the height of zone expressed in parts of an inch, accord¬ 
ing to the scale of the drawing. For example, suppose the 
scale to be and the horizontal curves to be 3 feet apart 
vertically, that is,., that the height of zone is 3 feet. Since 1200 
feet on the ground is represented by 1 foot of the drawing, we 
can write 1200 ft. = 12 in., or 100 ft. == 1 in., or 100 yds. = 3 
in., whence 1 yd. = inches, or .03 is the height of the zone 
according to the terms of the scale. Then the least width of 
zone (that for a slope of 1) will be .03 inches. The greatest 
width (or j\) will be .03x64, or 1.92 inches. By Buie 1 the 
greatest interval will be 

1 - 9 2 . + £, or, Mi=.13875 
16 16 


The least interval will be 

.03+ .3 .33 

•-— , or, — 

16 16 

which is .0206. And by Buie 3 the greatest thickness of the 
shading line will be % of .0206, or .0137. It will be observed 
that the actual height of zone is varied according to the scale 
of the map. This is necessary, in order to give room to express 
the curves of a steep slope on a small scale; and if the height 
of zone and the scale bear a proper relation to each other, the 


r 
























20 


intervals and thickness of the shading lines for a slope of 45 a 
will be nearly the same for all medium scales, only the max* 
imum intervals changing as the scale is enlarged or diminished. 
(See Figs. 17 and IS for examples on scales of -^Vo and 
respectively. The vertical distance of the curves is three teet 
in Fig. 17, and six feet in Fig. IS.) 

40. Although in both of the methods of treating lines of 
greatest descent, just explained, the theory of the convention 
is perfect, yet it is admitted that in practice an approximation 
only is obtained, inasmuch as a great deal is left to the judg- 



not only useful, but necessary, to have some fixed principles as 
a basis on which the art may be founded, and to which prac¬ 
tice may be conformed. The student ought, therefore, to make 
himself perfectly acquainted with the method (whichever it 
be) that he adopts, so as to present throughout his drawings a 
consistency in the expression of at least the relative degrees of 
inclination. For popular use, on ordinary occasions, this will 
be sufficient, as almost every one who is interested in looking 
at a topographical map, will have learned enough of the con¬ 
ventional signs to comprehend their general intention; while 
the scale of shade, or of spaces, which should always be put 
upon a drawing, will inform those who are disposed for a mi¬ 
nuter reading of it, if it is geometrically correct. 

41. But as it is not always possible, either for want of time, 
or for other reasons, to attempt a complete realization of the 
theory of these methods, it is proposed to exhibit their differ¬ 
ent modifications between strict conformity to the rules above 
stated, and those for rough or rapid sketching of the ground 
from nature. 

42. With regard to the English method, or that of vertical 
illumination, it has been remarked, in applying it in the ser¬ 
vice of the U. S. Coast Survey, that u this scale of shade does 
not represent slopes greater than 45°, thereby limiting the gra¬ 
phic capabilities and effect of the map. It also makes the 
slopes too dark as they approach the inclination of 45°, and 
does not well represent slopes of less than 5°, which latter it is 
often necessary and desirable to express distinctly.” A scale is 
then to be sought for by which the lower slopes may be readily 
distinguished from one another, and the graphic effect of tho 


♦ 


21 


high slopes retained. The slopes Ao to> and 55 or from 2^° to 
11 ° (about), are most frequently met with in those parts of our 
country not mountainous. Slopes from to T V, or from 14 ° to 
6 °, are such as are usually surmounted by roads. From a level 
to 25°, it is necessary to represent more slopes, and to represent 
them more distinctly than between 25° and 45°, and between 
the latter limits it is not necessary to distinguish nicely between 
every few degrees of slope. Between 45° and 90°, slopes should 
be represented for graphic effect, such as for clay banks, rocky 
precipices, &c., but it is not necessary to show their variation 
for any other purpose. 

43 . The scale then proposed, adapted to any part of our 
country, both for civil and military purposes, and as affording 
the means of graphic representations of all slopes useful for 
such objects, is the following modification of the scale of 
Par. 20 :— 

A slope of 14 ° is thus represented 
by the same thickness of shading lines 
as that of 2 i°, but the intervals should 
be doubled in the latter case, and so 
proportionally for any slopes less than 
24°. By this scale the slighter slopes 
are represented well, and will be readi¬ 
ly distinguished from each other. The 
shades for slopes less than 16° are dark¬ 
er than in the scale of par. 20 , which 
renders their differences more observable. From 25° to 75° the 
shades are lighter than the corresponding ones of the other 
scale, the distinction being here of less importance. The white 
space, for a slope of 75°, does not in this scale become too 
small for practical use. A scale in accordance with the pro¬ 
portions in the above table, may be constructed as is described 
in Par. 19, except that there must be eleven instead of nine 
divisions on A B, used for proportioning the black to the white. 
Its practical application is effected as in Pars. 21 and 22 , by 
repeated subdivisions of the proportion of black, until a pro¬ 
per thickness of shading line is arrived at. 

44 . A further modification of the scale of shade has been 
very generally adopted in England, which for ordinary pur¬ 
poses has the advantage c? simplicity, and facility of applica- 


Slope. 

Proportion of 

Black. 

White. 

2i° or 2f° 

1 

10 

5° or 

2 

9 

10° or 11° 

3 

8 

15° or 16° 

4 

7 

25° or 26° 

5 

6 

35° 

6 

5 

45° 

7 

4 

60° 

8 

3 

75° 

9 

2 









22 


tion. It consists in establishing with accuracy only three pro* 
portional quantities of black and white, for three medium 
slopes, viz. 15°, 22|°, and 30°, a level being represented by 
white, and a slope of 45° by bringing the shading lines in con¬ 
tact, or perfect black. Thus by Rule 2d, Par. 23, we have this 
table of slopes with their proportions of illumination :— 

A scale of shade may be at once 
constructed from this table, by assum¬ 
ing the thickness of the shading line 
for the medium slope of 22^°, which 
thickness must be suitable to the scale? 
and to the degree of fineness or finish, 
which it is intended to give the draw¬ 
ing. Having drawn this portion of the scale (as at A, Fig. 19) 
with equal proportions of black and white, diminish by one 
third the thickness of the black line for the part B of the scale, 
which will then correspond to a slope of 15°; and increase its 
thickness by one third for the portion C of the scale, which 
will represent a slope of 30°, white and black being respect¬ 
ively the extremes. This scale should be carefully applied to 
the map wherever the slope to be represented corresponds with 
one of the three in the scale. All intermediate inclinations are 
of course indicated by graduating the thickness of the shading 
line, referring it to the regulators in the scale. (See Fig. 35 for 
a drawing made according to the vertical system.) 

45. In the English and German method, and in all its modi¬ 
fications, the thickness of the shading line in the medium slopes 
(that is, where it is nearly equal to the interval between the 
lines), is an arbitrary quantity, and is regulated by the scale 
of the drawing, by the skill of the draftsman in mastering bold 
or fine lines, by the time that may be spent in drawing the 
many or the few shading lines required, Ac., Ac. Generally, 
if the lines have such a relation to the scale of the drawing* as 
to present a well connected appearance, it will be found that 
fewer shading lines, and a rather coarse texture will conduce 
more to clearness of expression when viewed at ordinary dis¬ 
tances, than a finer texture, which has a tendency to dryness 
of style. In the French method, however, as has been before 
remarked, the thickness of the shading lines and their intervals 
are both fixed by the scale of the drawing. 


Slope. 

Proportion of 

Black. 

White. 

level. 

_ 

all. 

15° 

1 

2 


1 

1 

30° 

2 

1 

46° 

all. 










23 


46. The scale of shade may evidently be still further simpli¬ 
fied, or, as in sketching in the field, it may be reduced to a 
mere graduation by the eye, of the color for the different slopes 
that offer themselves for description. As much of the data for 
topographical drawing, relating to extended civil works, is col¬ 
lected by sketching in the field, a few practical remarks on that 
subject will now be offered. 

47. Field sketches are made with the lead pencil, and may 
be drawn upon every page of the compass-book, or upon the 
alternate pages, at the option of the topographer. In the for¬ 
mer case, the bearings and distances are recorded upon the 
drawing {Fig. 16-|); in the latter, the record occupies the left 
hand page, and the sketch the opposite one. The page for 
sketching should be ruled in squares, with blue or red ink, 
forming thus an indeterminate scale, the length of the sides of 
the squares being assumed at pleasure, according to the nature 
of the ground. Both the record and the sketch are read from 
the bottom of the page upward. Suppose the stations of the 
survey to be one hundred feet apart; then, assuming the side 
of the square to be one hundred feet, commence the sketch at 
the bottom of the page—in the centre, if the survey promises 
to be tolerably straight; if otherwise, at some point to the 
right or left of the centre, the reason for which will be explain¬ 
ed directly. Let the bearing from the first station (the starting 
point or zero) be N. 10° E. {Fig. 16L) Draw a line from the 
bottom of the page upwards; the side of the square being as¬ 
sumed one hundred feet, number the stations upon the squares 
as far as the line is run, say three hundred and twenty-five feet, 
and write the compass angle down along this line. Let the 
bearing from the second station, or No. 1, be N. 1° W.; draw 
a line making, as nearly as can be judged by the eye, the pro¬ 
per angle with the last bearing, and proceed as before. When 
the page is exhausted, commence with a vertical line at the 
bottom of the next one, marking upon it the remainder of the 
old bearing, and making, by the eye, a new series of approxi¬ 
mate protractions as before. If it can be foreseen, as in most 
cases it can, that the line of survey will be very crooked, bend¬ 
ing, for example, from left to right, then commence the bear¬ 
ing at the bottom of the page accordingly, beginning at a point 
on the extreme right {Fig. 16£, dotted line), and ruling ltdia- 


\ 


24 


gonally to tlie left, so as to make due allowance for tlie great 
deflection anticipated in tlie next bearing. Such cases may be 
foreseen in running around an inclosure, or in following a curv¬ 
ing stream or ridge. The advantages of the system of squares 
in sketch-books completely overbalance the one disadvantage 
which is, that the diagonal bearings will not make exact dis¬ 
tances upon the squares, while the vertical and horizontal ones 
will. It will be remembered that the surveying book is design¬ 
ed to be exact only in its record and the general features of the 
ground, and that a slight change of scale is not material, as it 
can be made exact when the survey is protracted upon the map. 
By these approximate protractions, any page of the book of 
survey conveys a very just notion of the bearings and dis¬ 
tances, and of the relative positions of the general features of 
the ground. The first station being at the bottom of the page, 
{Fig. I 62 ,) note down in the space between it and the second 
one, all the features of the ground passed over by the line of 
survey; as to whether it is cultivated, forest, marsh, &c.; 
whether it is crossed by streams, ditches, &c., and their width; 
if it rises or falls, about what degree of slope, &c. On both 
sides of the line introduce, according to the scale, and their 
distances, as judged by the eye, all topographical objects within 
sight, such as buildings, roads, streams, hills, &c., &c., drawing 
them to the scale if possible, and if they cannot be got upon 
the page, describing briefly their nature and position. In 
sketching hills endeavor to project as many horizontal curves 
as possible, which should be lightly put in, and then the shading 
lines may be drawn over them. Tlie degree of slope should be 
frequently written down in numbers upon the sketch. Tlie 
names of localities, streams, hills, farms, &c., should also be 
entered. 

48. Thus far we have supposed a measured line upon the 
ground, to which the situation and dimensions of objects might 
be referred. It is much more difficult to embody the relative 
positions and dimensions, where all is left to the eye. Here a 
cultivated judgment is of the greatest value. Practice alone 
can make a good sketcher under such circumstances. Rules 
must, from the nature of the case, be few and general. In the 
first place, all objects within the field of vision are presented 
to the ey <3 in gyerspective, whereas the sketch is to be a plan. 




25 


The apparent diminution of dimensions in distant objects must 
therefore be corrected on the plan. For example, the windings 
ot a crooked stream, or a road, in perspective, are much exagge¬ 
rated in retiring into the distance; they must therefore be 
straightened out in the sketch, more and more, as they are more 
removed. 2nd. In looking at variously placed hills from a 
somewhat elevated station, the eye will in some cases look 
directly, or perpendicularly, at the face of some slopes, while, 
in others, the surface of the slope, if prolonged, will pass 
through the eye, and will not be seen in its true dimensions, 
though its inclination may be judged. In sketching the shapes 
of hills, bodies of water, masses of forest, &c., these facts must 
be taken into consideration, and to insure skill, eye-sketches of 
a small portion of ground having well-marked features, must 
be frequently made, and compared with measurements of the 
same features. In sketching a single hill, the best station is at 
the summit. First endeavour to represent the lowest horizontal 
curve of its surface ; then a medial one; then the form of the 
level space at the summit, or the highest horizontal curve. 
Others may then be introduced between these, until the ground 
is sufficiently expressed. The angles of inclination should be 
frequently noted down in numbers: all accidents of ground, 
such as ravines, rocks, &c., should be carefully placed, and all 
other objects, such as houses, fences, trees, &c., should be put 
down in their proper relative positions and dimensions. Hav¬ 
ing thus prepared a skeleton of horizontal curves, numbered 
as to inclination and heights, the sketch will always serve a 
useful purpose without any lines of greatest descent. After 
sufficient practice in this method, the eye will become so culti¬ 
vated as to enable the draftsman to express the form of ground 
by lines of descent at once, the mind conceiving the position of 
the horizontal curves, and thus supplying the necessary data 
for the shading lines, the relative thickness and length of which 
for the different slopes, is a matter very easy of acquirement. 
But this should not be attempted until the method by horizontal 
sections is thoroughly mastered. 

49. It is easy thus to make a correct sketch of a single hill, 
but when there are many, and the general face of the country 
is sloping also, the difficulties of representing the connexion of 
the different hills at their bases are considerable. In such cases, 


26 


the direction and lengths of the valleys (or water-courses if 
there are any) must first be noted, hearing in mind the illusions 
of perspective in both its effects, mentioned in par. 48. Then 
establish the positions of the different summits, marking down 
their relative heights, after which put in the other objects to 
be represented, such as roads, trees, buildings, &c., &c., refer¬ 
ring their positions to each other, and correcting them where 
they are found to disagree. Horizontal curves present the rea¬ 
diest means to the beginner in sketching declivities. When, 
after some practice, the form of a body suggests (as it always 
will) its horizontal sections (see Par . 11), then it will be time 
to resort at once to the lines of greatest descent. The greatest 
difficulties to be overcome in the practice of eye-sketching are, 
1st, that of converting a perspective view into a jplan, in all 
its true proportions; and 2nd, in forming a just conception of 
the intersections of different slopes at their bases . Hence the 
rule, to project first upon the sketch, all the lowest lines, or 
water-courses, and then the highest parts or summits. Then 
the middle lines and objects may be placed, and the sketch 
filled up by referring all others to those three groups which 
may be regarded as determined. 

50. The lead-pencil for field drawing should be moderately 
hard, and the general tone of the drawing should be rather 
light. The shading of slopes ought not to overpower by its 
depth the distinctness of other objects, and the pencil should 
be so used and of such a quality, as not to be easily defaced by 
rubbing. 

51. In concluding these remarks upon the methods of re¬ 
presenting hills by the conventional use of lines, drawn with 
pen or pencil, it is necessary to refer to the mode of expressing 
inclinations that are steeper than the “ natural slope,” or greater 
than 45°. Such slopes frequently occur in clay banks, steep 
ravines, and in rocks. As they are always exceptions to the 
law of slopes, and save in the case of rocks, cannot be regarded 
as a permanent form of the ground, since they are constantly 
undergoing reduction by the action of natural causes, the 
method generally adopted to show them, is to make their 
shading lines exceptional also. In the Horizontal System this 
is done in earth slopes, by shading them with a set of black 
and short lines drawn perpendicular to the horizontal sections: 


27 


that is, in a direction contrary to the general motion of the 
shading lines of the drawing. They should be made as black 
as possible. (Fig- 7, at B.) For the same kind of slopes in 
the Vertical System, their shading lines, also as black as pos¬ 
sible, are drawn parallel to the horizontal curves, or contrary 
to the general tenor of the shading lines of the drawing. {Fig. 
15, at A.) These methods answer also for the expression of 
occasional rocks, particularly projecting horizontal strata ; but 
when the slope is entirely rocky, even if it be not steeper than 
45°, the shading lines are thrown in, in every possible direc¬ 
tion, not intersecting, but abutting abruptly upon each other, 
in short heavy masses. {Fig. 15, at B.) 

52. The following are some practical remarks and directions 
for shading hills according to the Vertical System. All the 
preparatory pencil lines having been drawn lightly, and the 
spaces for the shading lines being laid off by dots, begin to 
shade at the steepest part of the upper zone of the hill. Draw 
the shading lines firmly, from curve to curve (introducing 
auxiliary curves for that purpose wherever it is necessary), so 
that each row of lines may terminate evenly at the lower edge. 
Draw always toward the body, turning the drawing on the 
table for that purpose. Draw these shading lines always down 
the slope , and proceed with them from left to right, so that the 
line just drawn may be uncovered by the pen, and the distance 
to the next one be seen. Go all around the upper zone in this 
way, finishing by joining the row at the point of setting out. 
This is always effected more easily and neatly in the steepest 
part of the slope. After finishing the first zone, proceed to the 
second, and so on to the foot of the slope. Where the curves are 
nearly parallel, the shading lines are straight, and also nearly 
parallel; but when the curves depart much from each other, the 
shading lines, being lines of greatest descent, must be normal 
to the curves, and will therefore themselves have some curvature, 
in order that they may tend perpendicularly upon a second 
curve, which is not parallel to the first. {Fig. 15, at C.) In 
such cases it is necessary, besides drawing the medial auxiliary 
curves, to put in lightly with a pencil, at short distances, a num¬ 
ber of normals {Fig. 15), which, being carefully studied, will 
tend to correct or confirm the directions of the shading lines as 
they are drawn. In introducing additional curves in those pai ts 


28 


of tlie liill where the slope is slight, care must be taken not to 
shorten too much the length of the shading line, for where the 
interval between them is large, the line must he proportionately 
liner and longer. (See Par. 33.) Any change in the direction, 
thickness, or proximity of the shading lines, required by the 
different inclinations, must be effected gradually, and all sud¬ 
den changes of that nature must be carefully avoided. Any 
two consecutive lines of any part of the hill, should be sensibly 
equal, similar, and parallel. They should be twin lines. The 
same thing is to be observed of contiguous zones; any change 
in their color or expression, must be made gradually. If it be 
required to pass from a light zone to a dark one below it, make 
the lower extremities of the lines of the light zone a little 
heavier, so that they may meet the upper extremities of the 
lower row, with nearly the same color. The latter may also 
be lightened a little. As zones differ in inclination, so of course 
will the spaces between the shading lines. No attempt there¬ 
fore ought to be made to prolong the lines of one zone into 
the zone below. The lines in each row are manifestly inde¬ 
pendent on each other in that respect. It is only necessary, as 
above stated, to avoid sudden changes of colour in passing from 
zone to zone. Even in a perfectly uniform slope, it will not do 
to prolong the lines thus, because it gives a hard and bad cha¬ 
racter to the style. But in the case of a conical hill, as in Pig. 
16, it would give rise to an error in principle; for we should, 
soon after leaving the summit, have too few lines of descent to 
cover the ground, and they would soon be so far separated as 
to lose their connexion, degenerating into a great meagreness 
of style. The same rules, in joining the different rows of lines, 
are to be observed here, as in the Horizontal System, viz. the 
extremities of one set of lines must not protrude within a 
neighbouring set {Fig. 20), nor must a vacancy be left {Fig. 21). 
The rows must be accurately joined, without showing either a 
white line at their junction, as in the latter case, or a dark one, 
as in the former (see Fig. 22). The method of joining them is 
shown in Fig. 23 on a large scale, where the lines of the lower 
row, coming between those of the upper, start from a line which 
connects the lower extremities of the upper row. When the 
whole plan of the hill has thus been covered with lines of 
greatest descent, the base and summit must be softened off*, by 


29 


tapering to a fine point the lower end of each line, at the base, 
and doing the same at the summit, by turning the drawing 
upside down, and tapering the upper end of each line of the 
upper zone (see Fig. 15). The whole hill being finished, the 
pencilled lines may be removed. The same directions here 
given for executing the drawing of a hill, will apply to a hol¬ 
low, the shading lines of which are converging. 

53. We will now proceed to consider the conventional use 
of lines in the representation of other features than hills, which 
alone have engaged our attention thus far; and 1st, of water. 
When the horizontal sections of the ground are continued, by 
means of soundings, below low water-mark, that part of the 
drawing covered by water must be left entirely white, so as to 
allow a clear exhibition of the lines of soundings, and the hori¬ 
zontal curves of the bottom, as determined by their means. 
But when the delineation of'the ground extends no further than 
the water surface, then for the sea, large lakes and rivers, the 
method of shading by lines drawn parallel to the shores, and 
graduated outwards from them, is generally used in the verti¬ 
cal system. This mode of proceeding would not answer in the 
horizontal system, as there would then be no distinction be¬ 
tween land and water. For the latter system, the method has 
been explained in par. 15. In order to execute symmetrically 
this style of shading water, the following directions must be 
strictly observed. After having drawn, with uniform thick¬ 
ness, a moderately stout line, as at A, Fig. 21, for the outline 
of the water, throughout the wdiole drawing, begin by apply¬ 
ing to it, as closely as possible, the first shading line. In order 
to do this, attend to the narrow white space between the two, 
making it a fine white line , and of even width. The first shad¬ 
ing line may be nearly of the thickness of the shore line, and 
should follow it closely in its minutest deviations. Apply such 
a line to every shore line in the drawing. When that is done, 
proceed to the second shading line, which may be a little finer 
than the first, and a very little more removed from it than the 
first was from the shore-line. Carry this one throughout the 
drawing, in the same manner as the first one. Then take up 
the third line, increasing, by very little, the distance between 
the lines, and drawing it a little finer. In this way, go on, 
adding one line at a time to every shore on the drawing, in- 


30 


creasing very gradually tlieir intervals, and diminishing, as 
gradually, their thickness. These lines should be drawn clean , 
and as steadily as the hand can make them. Take a very 
short hold of the pen, resting the point of the middle finger 
upon the paper. Each line should be of uniform thickness 
throughout its length, and kept constantly at the same distance 
from the one last drawn. Draw always towards the body, 
turning the drawing as before directed, and keep always the 
line last drawn to the left of the one in progress, so that the 
distance between it and the point of the pen may be con¬ 
stantly watched. The lines must be completed successively, as 
above directed, for the following reasons;—1st. The eye be¬ 
comes accustomed to the interval employed, and thus the con¬ 
fusion attendant upon carrying on at the same time, three or 
four lines having different intervals, is avoided. 2d. By this 
equal distribution of the lines, symmetry is insured, because 
whatever be the width of different channels (Fig, 24, at B), an 
equal graduation of tint from every shore is obtained, and the 
shading lines meet in the middle, which might not always be 
the case otherwise. 3d. It enables us to conform to a princi¬ 
ple, which is, that every line must return to itself \ and no spiral 
lines are admitted. But sometimes two lines will coalesce, as 
at g c, Fig. 24, where they join into one at c7, and afterwards 
separate into e e. The last line, in the middle of a piece of 
water, must be a line returning to itself, and not a spiral. 
When the shading lines meet the margin of the drawing, they 
are cut off; but they are drawn as if they were to be continued 
out of the margin. These instructions may seem over minute, 
but the beginner must be warned that this is the most tedious 
and uninteresting part of topographical drawing, and requires 
great care and patience, in order to produce a good effect. 
High and low tides are represented thus (Fig. 24). bis. Draw 
the shore line for the high water-mark, and the shore line for 
the low water-mark. Then commence from the high water 
line, graduating outwards until the low water line is met, which 
must be regarded as a margin for the shading lines, and in 
which they must terminate. Then commence anew from the 
low water-mark, with a new graduation, which is carried on 
uninterruptedly. 

54. Smaller bodies of water, such as ponds or pools, are 


31 


represented by a tint of fine, unbroken lines ruled across tliem 
parallel to the base of tlie drawing (Fig. 25). Rivulets, or 
very small streams are represented by one, two, or three 
lines, according to their magnitude (Fig. 25, at A, B, and C). 

55. The sign for marsh is composed of a mixture of the two 
signs for water and grass land, as in Fig. 26, where the water is 
indicated by fine and full lines, ruled always parallel to the 
base of the drawing, and grouped in an irregular manner, so as 
to leave small islands interspersed through it. These islands 
are filled with grass, drawn as will hereafter be described, with 
here and there a tree. The division between the land and 
water should be first sketched lightly with a pencil, as a guide 
for ruling the lines. The texture, as to fineness, of this sign 
should be regulated by the scale of the map, and be consistent 
with the other lines in it, in that respect. Distinctions have 
sometimes been made between salt and fresh marsh, deep 
morass, &c.; but this ruled sign is the neatest form, and does 
not charge the memory with nice distinctions, which can easily, 
if required, be expressed in small lettering, upon the drawing. 

56. Forest , being one of those features whose conventional 
sign is intended to suggest, in some degree, the object itself, is 
represented by characteristic lines, resembling a pen drawing 
of a tree as seen in horizontal projection, with its shadow upon 
the ground, cast by parallel rays inclined 45° to the horizon. 
The only distinction between the various forests, that can be 
recommended, is to reserve a particular sign for pines, and to 
include all other kinds in one character of foliage. Fig. 2T, at 
A, shows a pine forest, where the sign has a star-like form, and 
is darkened towards the right hand and lower side, where the 
shadow is placed. At B is the sign for all other forests, where 
the character of the outline is round, with a few touches of the 
pen on the interior, and towards the shadow. This outline, to 
have a good effect, should be made with simple curves, firmly 
drawn, and not be cut up by smaller indentations, as in fig. 27 
(bis), the bad forms of which are also to be avoided. The trees, 
and masses of trees, must be disposed in every possible variety 
of position, avoiding carefully all arrangement in lines, or 
regular figures. Their size depends upon the scale of the map, 
and should consist with the dimensions of buildings, the width 
of roads, &c. The sign in Figs. 27 and 7, at C, indicates an 


32 


ornamental grove, shaped by art, and is used in representing 
parks, gardens, Ac. Orchards are shown by placing single 
trees, with their shadows, upon the intersections ot two sets of 
equidistant parallel lines, drawn at right angles with each 
other, as in Fig. 28. One set of these lines is usually placed in 
the direction of one side of the inclosure. The lines should be 
drawn in pencil, and afterwards erased. Single trees are 
drawn, as shown in Fig. 29. The shadow is detached from the 
outline of the tree, and is intended to have an elliptical form. 
When the scale is small, a single tree becomes a simple circle, 
touched with the pen, on the side towards the shadow. Some 
topographers prefer to draw trees in elevation, as in fig. 30. 
This method certainly renders it easier to describe varieties of 
foliage, and may be used with as good effect as the other, 
according to the fancy of the draftsman. When trees occur 
upon a hill-side, the shading lines of the hill-side should be in¬ 
terrupted, in order to receive the body of the tree, but not its 
shadow, which may be drawn independently of them when the 
slope is slight; but when it is steep, the shadows may be 
omitted, and the trees must be shaded dark, so as to be nearty 
of the same color as the shading of the slope, and, at the same 
time, the forest may be represented as less dense than it is 
usually drawn upon a more moderate inclination. 

57. Cleared land , grass , or meadow , is indicated by groups 
of short lines, arranged like tufts of herbage. Each of these 
little figures is drawn with its base always parallel to the base 
of the drawing, whatever may be the shape of the inclosure 
containing this sign. They must likewise be spread evenly 
over the paper, not too thickly, and all appearance of regu¬ 
larity or approach to arrangement in lines must be avoided, 
as directed for forest (see Fig. 31). Each tuft is composed of 
from 5 to 7 lines, drawn as if converging in a point below 
the base, as is shown on a large scale at A—the middle lines 
being the longest, and the extremes mere dots. The base 
must be a straight line, not curved, as at B. 

58. Cultivated land is represented by alternate broken and 
dotted lines, suggesting furrows. These are, for the sake of 
variety, made to assume different directions, one set of them being 
generally parallel to one of the sides of the inclosure {Fig. 32). 
The ground must first be prepared by drawing light pencil lines, 


33 


equidistant from, and parallel to, each other, in sets. These 
pencil lines must he ruled, and if they cannot be spaced off by 
the eye, their intervals must be determined, and marked by 
dots. Then draw the broken and dotted lines by hand , over 
the pencilled guide lines. The joints in the broken lines must 
not be opposite to each other, and the breaks , or vacancies in 
the lines, must be very short. The dots of the dotted lines 
must be made by touching the point of the pen to the paper, 
and immediately lifting it off, without dragging it over the 
paper; this will make a round dot. The dots must be fine, 
and close together. As before remarked, it is scarcely neces¬ 
sary to distinguish between the different kinds of cultivation, 
as it is the most variable of all topographical features. If it be 
desirable to describe the existing crop, it can always be done 
by a few words, neatly lettered on the drawing. 

59. Uncultivated land , which is not forest, but such as 
brushwood, heath, prairie, &c., is represented by mixing tufts 
of grass with small bushes, of less dimensions than those of the 
trees in the sign for forest (Fig. 33). 

60. Sand and gravel are shown by dots—the latter rather 
coarser than the former. In making these, the pen should not 
be jerked over the paper at random, but slowly put down and 
taken up, and never without an intention in regard to the 
position of every dot. Make them as directed in cultivated 
land, and avoid all arrangements in lines (Fig. 7, at D). In 
sand-hills, let the sides of the slopes be made darker than the 
level parts, by making the dots closer together, in order to 
produce a deeper tint, or shade. 

61. The different forms of signs for buildings, inclosures, 
roads, Ac., &c., are given in Fig. 34. The equidistant lines 
representing a road, can, when curved, and therefore to be 
drawn by hand, be conveniently drawn thus :—Take a right¬ 
line pen, and open its two blades to the desired width of the 
road ; then place some India ink upon the inner face of each 
blade, in such quantity as not to allow the opposite masses of 
ink to run together. Then, if the pen be drawn over the 
paper, the two points will describe two equidistant lines. 

62. It must be remembered that the dimensions of all these 
signs are variable, and must correspond with the scale of the 
drawing. This just proportion may be gained in considering 

3 


34 


the projected dimensions of buildings, their class, as to being 
farm houses, mansions, public institutions, &c. ; for it would 
not be consistent to make a tuft of grass as large as a country 
seat or a college. 

63. All that lias been said in regard to the manner of execut¬ 
ing the conventional signs with a pen, will apply equally to 
sketches, or even finished drawings, made with a pencil or any 
instrument which produces lines. But there is another method 
of topography, now coming into very general favor, viz. that 
of expressing the different states or conditions of ground, and 
even its variations in level, by means of colors , the manner of 
using which will now be considered. 

64. The first thing necessary to be done, in order to prepare 
a sheet of paper for a tinted drawing, is to strain, or stretch it, 
so that it will not remain blistered after. being wetted by the 
laying on of the tints. For this purpose the paper must be 
moistened, and laid flat upon a smooth and clean board, and 
before it dries, the edges must he fastened down with glue, or 
very stiff paste. By moistening the paper, it is expanded, and 
if its edges are secured while it is thus enlarged, its shrinking 
in the act of drying causes the strain, which keeps it flat, and 
enables it to restore itself in drying, after it has been blistered 
by wetting. 

65.. Having thus prepared the paper, the lines of the draw¬ 
ing will be put upon it, first in pencil, and afterwards with a 
very fine ink line. The ink, although black, must not he 
thick; for, when the lines (outlines only) of all the shores, 
roads, buildings, &c., are drawn, and all the pencilled lines 
erased, then the drawing must be washed , either by exposing it 
to water dashed over it, or by quickly passing a soft sponge, 
well saturated, across its surface. This is done for the purpose 
of removing those portions of the ink, which a wet brush would 
detach from the paper in laying on the colors, and which, 
mixing with the tint, would injure its purity. When dried, the 
drawing will be ready to receive the conventional tints, which 
are expressed by the following colors, either used singly or 
compounded. 

66. They are five in number, viz. Indigo , Carmine (or Crim¬ 
son Lake), Gamboge, Burnt Sienna , and Yellow Ochre. In using 
and mixing these colors, it must be observed that Indigo is the 


\ 


35 


most powerful, and Gamboge the weakest; and that Yellow 
. Ochre does not combine well with any of the others, but is nsed 
alone. 

67. Before proceeding to consider the significance of these 
colors and their combinations, it is necessary to explain the 
mechanical conditions to be fulfilled, and the rules to be 
observed, in order to insure neatness and facility of execution. 
When a tint is to be mixed, let the end of the cake of color be 
wetted, and allowed to soften for a minute or two. This will 
cause it to rub smooth, and free from small fragments. Then 
moisten (only) a perfectly clean plate or saucer, and rub a suffi- 
. cient quantity of the color upon it, as much as will tinge to the 
proper intensity (say) three or four tablespoonfuls of water, 
which being added to the color, and mixed by the brush, the 
tint is ready for use. Let the paper be inclined about five 
degrees to the horizon, the lower edge towards the body. This 
is done that the color may flow easily over its surface, for the 
whole art of laying on a flat tint consists simply in allowing 
the colored water to flow over the paper, which is uniformly 
tinged as it passes over. To spread the color, begin with a full 
brush at the top of the figure (suppose it to be a rectangle), and 
cause it to lie neatly along the upper outline, then strike the 
brush from left to right, and from right to left, alternately, 
bringing the tint down in horizontal bands or stripes, control¬ 
ling it neatly and exactly within its proper outlines, and keep¬ 
ing the surface of the paper well wetted with the tint. As 
long as this is done, the tint can be carried on with perfect 
continuity. * On arriving near the lower outline of the figure, 
the quantity of tint must be diminished, so as to leave just 
enough in the brush to finish, without allowing the color to 
accumulate upon the lower outline. In no case, anywhere on 
the drawing, must the color be allowed to lie in puddles, or 
drops. The art of laying a flat tint is so easily acquired, with 
a very little practice, that the only difficulty in it is the out¬ 
line, to conform to which requires some care in using the point 
of the brush. When the colored water has once thus flowed 
over the paper, the tint is finished , and must not be touched 
again ; for if there be any little defect in it, one trial will show 
that any attempt to remedy it while the color is drying, will 
only make it worse. In laying tints of complicated shapes, the 


36 


operation is much facilitated by first moistening t-lie paper, and 
working upon it just before it dries. As tlie band acquires 
skill, it will be found that, generally, tints are better in pro¬ 
portion as they are more quickly laid on, and with less of color 
in the brush. Should stains or patches occur, however, they 
may be remedied by wetting the whole drawing, and gently 
washing the faulty parts with a brush or soft sponge, and 
repeating the tint lightly, should it be too much reduced by 
washing. Tints that are too strong may be rendered weaker 
by the sponge, in the same manner, and some may even be 
removed entirely. White spots left in a tint may be filled up, 
after it is dry, with the point of the brush, taking care not to 
apply the color where the paper is already tinted, as that would 
double its intensity, and make a dark spot. The knife should 
never be used for erasing on a tinted drawing, as the color 
sinks , and becomes intense, wherever the paper is scratched. 

6S. After the flat tint it will be necessary to practise the 
ciltei'nate or double tint. This consists of two colors, applied 
alternately, their edges being allowed to melt into each other. 
For this purpose, two saucers of tint must be prepared, with a 
brush for each. Begin, as for a flat tint, with one of these 
colors, at the upper outline of the figure, and having laid on a 
small portion of that tint, take the brush charged with the 
other color, and before the first dries, run around its edge with 
the second, and allow them to blend together, then resume the 
first tint, blending in the same manner, and so on throughout 
the space to be filled. It will be observed that the surface of 
the paper is here treated exactly as if a flat tint were being 
laid, the color not being allowed to dry anywhere. Each tint 
is spread upon the white paper, and therefore shows itself pure. 
The forms of the masses of each color should be varied, and 
not made in stripes, or spots, but irregularly clouded. The 
tints in this sign should be light, and equal to each other in 
strength. 

69. For the use of the colors as follows, see Fig. 36:— 

Water, a flat tint of pure Indigo, light colored (a). 

Sand , a flat tint of Yellow Ochre (b). 

Cultivation , a flat tint of Burnt Sienna (c). 

Grass Land , or cleared ground , a flat tint of green, composed 
of Indigo and Gamboge, the latter predominating (d). 


37 


Uncultivated Land , or Brushwood , a double tint of alternate 
green , as for cleared land, and Burnt Sienna, laid on as de¬ 
scribed in _P<zr. 68. This sign may also be made with alternate 
Green and Crimson Lake, it being the only double tint used (e). 

Buildings , and in general all masonry, such as bridges, locks, 
walls, &c., are tinted with Crimson Lake, and shadowed with 
a neutral mixture of Indigo, Burnt Sienna, and a little Lake. 
For this, and all other purposes of light and shade, as in forest, 
&c., the light is supposed to enter the drawing at the upper 
left hand corner of the margin, in parallel rays, inclined 45° to 
the horizon. The shadow of any object will, therefore, sur¬ 
round its lower and right hand outlines. After the shadow has 
been placed, the outlines must be strengthened, by making it a 
heavy black line on the sides opposite the light (f). This re¬ 
inforcing the outline is always the last work on the drawing, 
and must never be undertaken while any brush-work or tinting 
remains to be done. 

Moods , streets of towns , and all portions of the drawing not 
particularly described, are tinted with Yellow Ochre. 

70. In the signs for Forest and Marsh , some attempt is made 
at a resemblance to the things signified, and a more minute de¬ 
scription of the method of executing them will be required. 
For forest {Fig. 36, g) the ground is first prepared by laying a 
flat tint of green, exactly as for cleared land. Then with a 
very hard and sharp lead pencil, or a pen with pale ink, groups 
and masses of trees are drawn in outline, as described in Par. 
56. Then, with Indigo and Gamboge, mixed in the brush to 
the same tint as the ground color already laid on, but a little 
more intense, each tree and mass of foliage is shaded on the 
right hand and lower portion. An orange tint, made of Gam¬ 
boge and Burnt Sienna, is then touched upon the side next to 
the light. These two tints should just fill up the outline, the 
green occupying about two thirds of the figure. This finishes 
the tree. It only remains to add the shadow upon the ground, 
which is made and laid on as directed in Par. 69. For single 
trees, as in orchards, the shadow is detached , but in masses of 
foliage, it is laid close to the outline (h). The above is merely 
a formula for this sign, but there is always an opportunity for 
the taste of the draftsman to produce a good effect, by present* 

in a- trees somewhat in the manner of landscape painting. 

o 


38 


71. Marsh , as in pen-drawing, is composed of a mixture of 
the signs for water and cleared land, which interlace horizon¬ 
tally, that is, always parallel to the base of the drawing (i). 
The green tint of marsh is first to be laid in with a brush mode- 

O 

rately charged with the color for cleared land. In doing this, 
attention must be paid to that part left white, which latter must 
be rather less in quantity than the green, and must resemble it 
in form, projecting its horizontal points into the green, just as 
the green projects into the white. The outer limits of a marsh 
must be made up of an outline of projecting green points. 
When that is done, a thin shading line must be drawn along 
the lower edge of the green. This is composed of Indigo and 
Burnt Sienna, and must be confined within the limits of the 
green tint, and not allowed to touch the white. This finishes 
the land portion of the marsh. The water is represented with 
very light indigo, laid on in horizontal streaks of varied width, 
just filling up the white space without encroaching on the 
green. The introduction of a single tree here and there assists 
the good effect of this sign. 

72. In painting the trees in forest, and shading the banks of 
marsh, &c., it is not necessary to mix tints in a saucer. It will 
be sufficient to rub the three colors, Indigo, Burnt Sienna, and 
Gamboge, side by side upon the same plate, and with a proper 
quantity of water in the brush, to mix them to the proper color 
and intensity, so that they may be applied without lying in 
drops upon the paper. 

73. In regard to the representation of slopes and declivities, 
the principle heretofore laid down, viz. a steep or a gentle slope 
being indicated by a darker or lighter color, must be here fol¬ 
lowed. The tint used to replace that produced by the pen¬ 
lines, is composed of Indigo and Burnt Sienna, when the ground¬ 
work is green; and when used over sand, or cultivation, a little 
Lake is added to the mixture in order to neutralize its greenish 
hue. This shade tint is always laid on after the ground is 
covered with an appropriate sign, and as no hard edges can be 

admitted, the following method is used to avoid them (k):_ 

With clean water in the brush, moisten well the paper aloim 
the line of the crest of the slope, and before it dries begin in 
the lower edge of the moistened part to lay on the shade'of the 
slope. Proceed down the hill with it, laying it on like a flat 


39 


tint, until tlie lower limit of the slope is reached, when, while 
the shade tint is still moist, it must he softened off, or blended, 
with a brush and clean water. If the slope be of great hori 
zontal extent, its sides may be shaded in successive portions- 
provided no hard edges are left on the tint, because a slope can 
never be finished by once tinting, but recpiires repeated touch¬ 
ing, so that the proper depth of shade may be procured, and 
so that all the detailed variations of declivity may be indi¬ 
cated by corresponding degrees of intensity. Then if the 
joints of the tint are made in different places each time of 
going over, they will not show themselves. This method of 
representing hills is very expeditious, but its effect can be 
much improved by the addition of light shading lines drawn 
with the pen, either with pale ink, or a mixture of Burnt 
Sienna and Indigo. 

74. In reference to the general effect of these tinted topo¬ 
graphical drawings, two things are to be considered in the 
colors, viz. the quality of the mixed tints, and the strength or 
intensity of color. Greens should not be of a cold quality, 
such as is produced by too much blue, but of a lively hue, 
which is produced by a predominance of Gamboge. As to in¬ 
tensity, everything should be subordinate to the condition of 
v clearness ; next, the tints must be clean, transparent, and rather 
light, so as not to mask any of the details of the drawing. 
They must be of sufficient strength, however, to be readily dis¬ 
tinguished from each other at once, and even a very little 
stronger than necessary so as to allow for fading. 

All tints that are much extended ought to be balanced , that 
is, no one ought to obtrude itself upon the eye by its too great 
intensity. According to the terms of art, everything should 
be “ in keeping,” and sj)ottiness avoided. Thus forest, brush¬ 
wood, and cultivation, ought to be kept about equal in strength. 
Cleared land, marsh, sand, and water, may be made of equal 
intensity, but all a little lighter than the other signs. Tints 
that are of small extent, may be a little exaggerated in inten¬ 
sity in order that they may be readily distinguished. Build¬ 
ings, being objects of small extent, and having a certain im¬ 
portance, require a well marked red tint, shadow, and shaded 
outline. Tillages, with their gardens, orchards, &c., should 
generally be represented a little stronger in the tints that com- 


40 


pose tliem, than the general tone of the surrounding cou itry 
{Fig. 36, at m). 

75. The order in which the tints for the different signs are 
successively laid on, is a matter for the experience and skill of 
the draftsman to decide. It is generally thought better, in or¬ 
der to insure a proper balance among them, to begin with the 
lightest. 

76. Cultivated ground is sometimes striped (Fig. 36, at c) in 
the manner of furrows, with lines of red, yellow, blue, or green, 
lightly laid on, and in various directions. 

77. Inclosures are represented as follows. Hedges by green 
dots, varied in size, for bushes, with the shadows. Masonry or 
brick walls, by a line ruled with red. Wooden fences, bylines 
either ruled or hand-drawn with a pen, containing the neutral 
mixture of Indigo, Burnt Sienna, and Lake (n). 

78: After the delineation of all the topographical features 
heretofore described, the next most important labor of the 
draftsman is the lettering of his map. And in this department 
his responsibility as to the good appearance of his drawing is 
very considerable, for nothing so surely detracts from the value 
of a map, viewed as a work of art, as an awkward and un¬ 
handsome style of lettering. To make manuscript letters, imi¬ 
tating type-printing, requires a great deal of study and prac¬ 
tice, and to proportion the title and other lettering, so as to suit 
the scale and general effect of a map, is a matter of considera¬ 
ble importance. As far as written directions can be of service 
in guiding the draftsman in this part of his work, the following 
rules may assist him : 1st, as to the time for lettering. If the 
map is a pen drawing , all letters that fall upon the surfaces of 
lakes, rivers, &c., or upon the sides of steep hills, or in a forest, 
should be put upon the drawing before those features are 
drawn, for it is easier to pass their characteristic lines over the 
letters, than to draw the letters upon the paper already so oc¬ 
cupied. In a tinted drawing , the letters are always the last 
drawn, as a brush cannot be passed over them without blotting. 
2d, as to the size of the letters. This depends upon two things; 
the importance of the object described, and the scale of the 
drawing. The different characters or types of lettering em¬ 
ployed, are thus arranged in regard to importance: 1st, the 
upright capital; 2d, the inclined capital; 3d, the upright Bo- 


41 


rn/rn, or ordinary small type; and 4th, the small Italic. The 
first of these characters belongs to such objects as large cities, 
an extensive forest, a bay or gulf, an island, or a considerable 
mountain or river. These same objects, when they are of less 
importance, may be described in inclined capitals, as may also 
a village. A road or canal, in Roman small type, and farms, 
residences, &c., in Italics. In regard to proportioning the size 
of the letters to the scale of the drawing, the following table 
will serve as a general guide, which is all that can be pre¬ 
tended, as an acquaintance with the way in which this propor¬ 
tion is arranged in drawings of merit, will furnish the best rules 
of practice:—* 



Scale. 

Height of upright 
Capitals. 

Height of small Roman. 

1 

600 

or one in. to fifty ft. 

Six-tenths of an inch. 

Twelve-hundredths of an in. 

1 

2640 

or two ft. to one m. 

Four “ “ 

Eight “ “ 

1 

5230 

or one ft. to a m. 

Three “ “ 

Six “ “ 

1 

10560 

or four in. to a m. 

Two “ ** 

Four “ “ 


The variation in height for each scale, from that of the upright 
capital to the italic, is gradual, and is regulated as above stated 
by the importance of the object. The thickness of the capi¬ 
tals, in proportion to the size, is one seventh of the height of 
the letter. In lettering a drawing, it is desirable that all the 
names should be in lines parallel to the base. Rivers, roads, 
canals, &c., sometimes require the line of the letters to be both 
oblique and curved ; care must be taken, in such instances, to 
place it so that the words may be easily read without turning 
the drawing. 

79. The formation of the letters requires great attention and 
study. The beginner must copy from good models, all the 
different kinds of character, and thus acquire a perfect know¬ 
ledge of the proper proportions and expression of every letter, 
both large and small. He must then exercise himself by draw¬ 
ing them without a model, in order to acquire manual skill, 
which he cannot be said to have done until he is able to form 
all the letters correctly, and give them their proper symmetry 










42 


and family resemblance, having for a guide only the two pen¬ 
cil lines which limit their height. In making capitals, eacn 
letter must be fairly sketched in pencil, including the thick¬ 
ness of the heavy parts; the outline must then be drawn in ink, 
with a firm and steady line, and afterwards filled up with 
the pen. Whether capitals are upright or inclined, it is w T ell 
to draw a few lines in pencil, parallel to the direction of the 
letters, which will serve as guides in drawing them. When it 
is required that one or more words shall occupy a certain place 
on the paper (as in titles of maps, wdiere the middle points of 
the lines lie upon a vertical line), find the middle letter or 
space, and put it in its proper position, then draw the latter 
half of the word or line. Proceed from the centre to the left, 
and draw in the first half, by putting in the letters in inverse 
order. This method often saves repeated trials and erasures. 
For drawing the small roman and italic letters, the same kind 
of study with the pencil is at first required ; but as the heavy 
parts of these are made at once, by a bold pressure upon the 
pen, the operation of making them resembles careful writing. 
As a preparation, three pencil lines are drawn, the lower two 
to form the upper and lower limits of the ordinary letters, and 
the upper one to limit the capitals and the tops of the Z’s* W s, 
&c. The parts of these letters are of two kinds, viz. : curved 
and straight , which should be carefully distinguished from 
each other. For example, a , c, g , <?, s , &c., are composed en¬ 
tirely of curves. They must be symmetrically drawn, and the 
width of the ordinary letter must be only a little less than its 
height. The round part of a g does not reach quite to the 
lower line. The letters 5, d,f ’ h, m, n, p, q , &c., are composed 
both of curved and straight parts. The uprights of these 
letters must be made perfectly straight from top to bottom, 
with a little horizontal return, pointing to the left at the top, 
and at the bottom to the right. The m and n, although curved 
at the top, must be brought down straight to the lower line, 
with a return pointing to the right. These returns must always 
form a sharp angle with the line of the letter, and not be 
rounded. See Fig. 37 for the application of these rules. The 
letters i , Ic , Z, -y, w, x , and 3 , being composed entirely of right 
lines, care must be taken to keep their elements straight. The 
beauty of this kind of manuscript depends more upon the 


43 


regularity and mutual likeness of the letters, than upon their 
individual character. In italics, the inclination of the lines 
must he everywhere the same. As compared with clear 
roman or italic type, manuscript lettering ought to occupy 
rather more horizontal space, and always looks better when 
somewhat extended; crowding it injures its effect very much. 
The little returns at the top and bottom of the straight parts 
may also be inclined a little from the horizontal, the left hand 
extremity of it pointing a little downwards. When executed 
with freedom and regularity, there is a peculiar beauty in let¬ 
tering with the pen, which does not depend upon a resem¬ 
blance to printed work. Finally, the merit of a map as to 
accuracy even, is not safe from doubt, when, however correctly 
drawn, its style of lettering marks a want of knowledge or 
skill in so simple a matter as the formation of the letters of 
one’s language. 

80. A map being drawn and lettered, to complete it there 
are required a border, a descriptive title, and the meridian 
line, and the scales. 

81. First. The border. The taste and fancy of the drafts¬ 
man may sometimes suggest such a composition of lines or 
figures for this purpose, as will greatly embellish a drawing; 
but if a plain one is required, the style generally adopted is a 
double line, one heavy one on the exterior, and one light inte¬ 
rior one, the heavy line having the same breadth as that of the 
blank space between it and the light line. As the map is gene¬ 
rally a rectangle, the rule usually followed for proportioning the 
breadth of the border (including the two lines and the space 
between them) is, to make it the one hundredth part of the 
length of the short side of the rectangle. A quill pen, with a 
very broad point (cut off, not square, but by inclining the 
cutting instrument towards the body), and without any split, 
is the best instrument for drawing very broad ink lines. 

82. Second. The title . This may be placed outside the bor¬ 
der, if it takes up only one line ; but if it requires several, then 
it must be placed within it. The letters composing the name 
of the locality , which is generally the most important word, 
should not exceed in height three hundredths of the length cf 
the short side of the border. The letters of other words are 
varied in size according to the importance of the words they 


44 


compose. The execution of the title furnishes another oppor¬ 
tunity to enhance by its ornamental character, the beauty of 
the drawing. It ought to occupy one of the corners of the 
map, and to have the middle points of all its lines of words or 
phrases, upon a vertical line. It should state, in small letters, 
the name of the draftsman, the dates of the surveys, and of the 
drawing, and under whose direction executed. 

83. Third. The meridian , or north and south line. This is 
an indispensable adjunct to every topographical drawing or 
map. When the extent of country represented is very consi¬ 
derable, it is generally managed so as to make the top of the 
sheet the north side of the limits. The upright sides of the 
margin are then north and south lines, and the word “ north” 
may be written outside and above the upper border. But if 
the shape of the ground included does not conveniently admit 
of this arrangement, then a meridian line must be determined, 
and projected upon the map. The importance of this line is 
evident, as without it no just idea of the situation of the loca¬ 
lity with reference to the surrounding country can be obtained ; 
nor could the drawing be compared, or used in connexion with 
any other map, unless it has this fixed line of direction, which 
is common to all. The true meridian cannot be determined by 
the magnetic needle, which does not always point to the geo¬ 
graphical pole ; but the following is a very easy way of find¬ 
ing it by means of a plummet and a watch. At some point 
laid down upon the map, suspend a plumb-line over a table, 
which has been made exactly horizontal. The line should 
hang from the very extremity of a pointed rod, which should 
be inclined about 45° to the table, and directed towards the 
north. The plumb-bob should have a sharp point, which must, 
as nearly as possible, touch the table. At any two moments 
equally distant before and after twelve o’clock, say at 9 A.M. 
and at 3 P.M., mark exactly the extremity of the shadow cast 
by the rod, and from each of these points draw a line to the 
point immediately under the plummet. A line bisecting the 
angle formed by these two lines, will be a true meridian, if 
the watch indicated the true noon, and has not altered its rate 
of going between nine and three o’clock. It is easy to prolong 
the line thus formed, and to project it on the map, either by 
finding upon its prolongation some other point laid down on 


45 


the map; or if there he none, by measuring the angle between 
the meridian and a line joining the plummet, and some other 
known point laid down. The meridian may be found without 
using a watch, by marking the extremities of two shadows of 
equal length, one cast by the sun before, and the other after 
noon. It is usual to make the meridian line a conspicuous one, 
and to ornament its north extremity with some fanciful device, 
though a simple arrow-head, with the letter N, will answer all 
the purpose. 

84. Fourth. The scales. Every drawing should have two 
scales—one the scale of spaces , from which to deduce the 
degree of declivity, as explained in Petr. 34, and the other, the 
scale of horizontal distances. They should be carefully mea¬ 
sured and drawn upon the map, in any convenient position 
within the border. For the scale of distances, the length of 
line measured ought to be between a fourth and a third of the 
long side of the border. 

85. The conventional signs for bridges, roads, &c., and other 
topographical minutiae, are exhibited in Fig. 34. The nature 
of each object there represented may, if desirable, be further 
explained by descriptive lettering; for example, a mill, or fac¬ 
tory, being indicated by the proper general signs for such ob¬ 
jects, can better be described in letters as a flour-mill, or cloth 
factory, &c., than by making a different sign for every kind of 
mill. Numerous signs, differing, as they must, very little from 
each other, are either a heavy burden to the memory, or are 
unintelligible -without an explanatory table. 

OF SCALES. 

Before projecting upon a map the data collected by a sur¬ 
vey, it is necessary to decide upon some scale of horizontal 
distances, suited alike to the purposes for which the map is 
intended, and to the nature and amount of detail that it is 
required to represent. If the scale is too small, it banishes 
many details that might be desirable; if too large, it produces 
an unwieldy drawing. In order that a scale may be a conve¬ 
nient one for use, it is necessary, on the one hand, that the 
dimensions measured on the ground should be converted, with¬ 
out calculation, or by an easy effort of the mind, into the cor- 


46 


responding dimensions on tlie map ; and on the other liana, 
that the dimensions of the ground should be just as easily in¬ 
ferred from those of the map. 

For example, in the scale of one foot to a thousand feet, or 
ToV 05 one hundred feet of the ground is represented by one- 
tenth of a foot on the map, or . 1 , one hundred and fifty feet by 
.15, and one hundred and seventy-eight feet by .178, or 178 
thousandths of a foot, which bears so close a relationship in its 
figures, to the distance measured on the ground, that it can be 
at once taken in the dividers from a scale, which will hereafter 
be described. On the contrary, a scale is inconvenient for use, 
when the denominator of its ratio is such a number as T gVo j or 
eight inches to a mile, or which is six inches to one 

mile. The long measure used in our country, viz. miles, 
yards, feet, and inches, has been the means of retaining these 
arbitrary ratios in use among our draftsmen, but in the service 
of the United States Coast Survey, the decimal scale is adopted 
for all maps. The French long measure being expressed en¬ 
tirely in decimals, makes the application of the decimal scale 
perfectly appropriate; but with us, it is easier to estimate dis¬ 
tances by miles, half miles, and yards, than by thousands or 
hundreds of feet. It is proposed to treat of both these kinds 
of scales, and to show how arbitrary ratios may be expressed 
by a diagonal scale of equal parts. 

There are two scales to be constructed for a map:—One, the 
scale of distances, which the draftsman puts upon the drawing 
after it is finished, and which is used only in finding and com¬ 
paring distances on the paper; the other, the scale of construc¬ 
tion, intended to furnish the smallest measurements that may 
be required in projecting dimensions on the drawing. 

To construct the scale of distances {Fig. 38), draw a right line 
with the pencil, and supposing, for example, the scale to be 
ToVoj divide it into equal parts, each one tenth of a foot in 
length. This ought to be done with the graduated edge of a 
good scale, for though the compasses would give equal divi¬ 
sions, yet we could not be sure that each one was exactly - 1 - of 
a foot, or that the sum of ten of these would be exactly equal 
to^ one foot. Above these points of division write the numbers 
0 , 100 , 200 , 300, &c., to 1000 . Then 2000, 3000, &c., at intervals 
of a foot. Prolong the measured line on the left of the zero 


47 


and lay off the distance of one tenth of a foot, which must he 
divided into ten equal parts, and numbered in their order from 
the zero to the left. Put this line in ink, and draw beneath it 
a heavy line, say two-liundredths of an inch wide, and at a dis¬ 
tance below the first line equal to its width. This heavy line 
should not pass to the left of the zero of the scale. Then with 
a right-line pen, rule the divisions before measured off, drawing 
them perpendicular to, and across both lines of the scale. If 
it should be required, for example, to take from this scale a 
distance of 180 feet, place one foot of the dividers upon the 
point marked 100, and carry the other beyond the zero to the 
left, until it comes to the division marked 8°. The compasses 
will then include the required distance. Any odd number of 
feet will be found by supposing each of the small spaces on the 
left of the zero to be divided into ten equal parts, and placing 
the foot of the compasses accordingly. 

The scale of construction (Fig. 39), being intended to express 
smaller dimensions than the scale of distances, which, it will 
be observed, shows nothing smaller than hundredths of a fix »t, 
is constructed as follows. After having subdivided and num¬ 
bered a right line as before, let fall perpendiculars from , every 
point of division, then draw ten other lines below, and parallel 
to the first, equidistant from each other. This equal spacing 
may be two tenths of an inch, or less, or more, provided it be 
constant for each space, blow in the space of the T V oi a 
foot which lies on the left of the zero, draw the diagonal lines, 
as in the fig., by joining the first division on the left of zero 
(the point c) with the point &, and drawing through the points 
20 , 30, 40, &c., lines parallel to b c. From this construction, and 
the properties of similar triangles, it is evident that that part 
of the line AB (the second line from the bottom), which is in¬ 
cluded between the sides of the triangle o be, is equal to one- 
tenth of o c, the base of the triangle; that the corresponding 
part of the third line, CD, is equal to two-tenths of the base, 
o c, of the fourth line, it is equal to three-tenths, and so on. 
But the base, o c , of the triangle is the part of a foot, 
therefore the parts of the horizontal lines intercepted by its 
sides are, respectively, y’oVo? tioo? tvoo> &c., of a foot, which 
fact is expressed by the figures 1, 2, 3, 4, &c., upon those lines. 
If it be required to find from this scale, a distance of 277 feet, 


• 48 

place one foot of the dividers at d, on the vertical line num¬ 
bered 200, and upon the horizontal line numbered 7, then place 
the other foot at e at the intersection of the same horizontal line 
with the diagonal numbered 70, and the distance will corres 
pond to 277 feet This is called the diagonal scale- of egualparts , 
and a scale thus constructed is applicable to all decimal ratios, 
the numeration only changing with the ratios. If the distances 
are expressed in other terms than in feet, the top line of the scale 
must be divided according to those terms. For example, if the 
scale were one inch to a hundred feet, the upper line of the 
scale must be divided into inches, and the inch on the left of 
the zero into tenths. Then the ten horizontal lines, and the 
diagonals, will express hundredths of an inch, or one foot on 
the ground. If, instead of using brass or ivory scales, the 
draftsman makes the scale himself, which is to be preferred, it 
must be made upon a piece of the same paper as the draw¬ 
ing, so that there will be no unequal variations in the scale and 
drawing, caused by heat or moisture, which affect different spe¬ 
cimens of paper very differently. 

Other ratios may be expressed on the diagonal scale by the 
following method: Suppose it is required to construct a scale 
of 24 inches to 1 mile, which shall be capable of measuring 
anv odd number of feet. The ratio of this scale is that 

•J J. t) 4 U 7 

is, one foot of the drawing corresponds to 2640 feet on the 
ground. Then one inch of the drawing (and of the scale to be 
constructed) corresponds to or 220 feet, and one-tenth of an 
inch to 22 feet. Draw the line of the scale as before ( Fig. 40), 
divide it into inches, and number the points of division from the 
zero to the right, 0, 220, 440, 660, 880, &c. Divide the inch 
on the left of the zero into ten equal parts, and number them 
0, 22, 44, 66, 88,110, &c., from the zero towards the left. FTow 
draw eleven parallel and equal-spaced lines below the first one, 
and draw the diagonals in the space on the left of the zero. It 
is evident, from an inspection of this scale, that the parts suc¬ 
cessively cut off upon the horizontal lines by the sides of the 
triangle obc are, commencing from the line next to the lowest, 
respectively equal to T V, t 2 t> tt? &c., of 22 feet, or the base of 
the triangle, which is one-tentli of an inch, or in other words, 
they are respectively equal to 2, 4, 6, 8, 10, &c., feet. Single 
feet are found by placing the compasses midway between the 



49 


horizontal lines. This scale is very much inferior, in point of 
convenience, to the decimal scale, on account of the compli¬ 
cated numbers which express its divisions, the addition and 
subtraction of which cannot be readily effected by a mere men¬ 
tal operation. Other scales may be constructed as follows:—12 
inches to a mile, or s 2V0 : Divide the line into inches, and num¬ 
ber the divisions 0, 440, 880, &c. Divide the inch on the left 
of the zero into eight equal parts, each of which will be 55 
feet; draw eleven lines below and parallel to the first line, and 
draw the diagonals. The parts cut off on the horizontals by 
the sides of the triangle, will be successively 5, 10, 15, 20, &c., 
feet. 8 inches to 1 mile, or : Divide the scale into inches, 
and the left hand inch into ten parts. Draw eleven horizontal 
lines below, and the diagonals ; the parts then cut off will be 
6 , 12, 18, 24, &c., feet successively. 6 inches to 1 mile, or 
To jfo* Divide the line into inches, and the left hand inch into 
eight equal parts. Draw eleven horizontals. The distances cut 
off will be 10, 20, 30, 40, &c., feet. 4 inches to 1 mile, or ¥ • 

Divide the line into inches, and the left hand inch into eight 
parts. Draw T eleven horizontals, and the distances will be suc¬ 
cessively 15, 30, 45, &c., feet. The subdividing qualities of all 
these scales may be increased by augmenting the number of 
the horizontal lines. For example, in the scale of 6 inches to 
1 mile, if there were 22 horizontals instead of eleven, the suc¬ 
cessive distances would be 5, 10, 15, 20, &c. If the horizon¬ 
tals were doubled in number in that of 8 inches to a mile, the 
distances would be 3, 6, 9, 12, &c., and if they were trebled in 
the scale of 4 inches to a mile, or made 33 in number, we 
should have distances of 5, 10, 15, 20, Ac., feet. 

The reason for drawing eleven horizontals in some of the 
above described scales is, that the number 11 is an exact mul¬ 
tiple of the number of feet represented by the divisions of that 
part of the line on the left of zero. A great multiple ought 
to be selected, so as to have a convenient number of horizon¬ 
tals. To take one more example. 5 inches to 1 mile, or n | T 2 : 
Here one inch of the scale corresponds to 1056 feet, or § of an 
inch to L ^- 6 = 132 feet. We divide the inch on the left of the 
zero into eight parts, and for the number of horizontals we 
seek the largest desirable factor of 132, which may be either 
22 or 12. If we draw 22 horizontals, the distances given by 

1 



t 


50 

tlie diagonals will be 6 , 12 ,, 18, 24, Ac., but if 12 horizontals 
are used, they will give distances of 11, 22, 83, 44, Ac., feet. 
It is evident, also, that the inch on the left of zero must be so 
divided, as that the number of its equal parts must be a multiple - 
of the number of feet corresponding to the inch, as above. 
1056 is a multiple of 8 , and not of 10, hence we divide the 
inch into eighths, each of which is 132 feet. 

Unless these multiples can be found, the scale cannot be made 
to express whole numbers by its smaller divisions, which is a 
great defect. It is to be hoped that the decimal scale and ratio 
will eventually be adopted. 

In adopting the scale to the uses of a map the following ge¬ 
neral proportions may be observed: A map constructed on a 
scale of half an inch to a mile, or TH Vio > will admit the repre¬ 
sentation of all towns, villages, main roads, the principal cross¬ 
roads, and every considerable mountain and stream. On a 
scale of one inch to a mile, or ¥ ^besides these, farms, 
woods, isolated buildings, every stream of 600 feet in length, 
and every hill of a hundred feet in height, can be represented. 
On a scale of two inches to a mile, or the various fea¬ 

tures of the ground can be clearly and accurately presented, 
also every stream of not less than 300 feet in length, every 
pond of more than 50 feet broad, besides all roads, isolated 
buildings, Ac. The scale of six inches to a mile, or T oT 6 o> is 
well suited for the complete delineation of a country. Scales 
for projecting experimental surveys for civil purposes very sel¬ 
dom exceed twelve inches to a mile, or • Larger scales 
than these are only used in proportion to the amount of detail 
required. The decimal scales corresponding nearly to these 

i" 2 o~o'o"cr? 6 olooj 30 I 0 o? to 0005 and jo'Vt* The smallest publi¬ 
cation scale of the U. S. Coast Survey is T 0 L 005 which is also 
the scale of the new map of France.* 


OF MERIDIANS AND PARALLELS OF LATITUDE. 
In a very extended survey, where latitude and longitude are 


* The reader is referred to the beautiful maps of the United States Coast 
Survey, and to the very elegant detailed map of France, both in course of 
publication, as admirable illustrations of topography. 


1 



51 


considered, it is necessary to project the meridians and paral 
lels upon the map. If the portion of the country included in 
the survey does not exceed one hundred miles in length and 
• breadth, no appreciable distortion of outline will be occasioned 
by drawing straight lines at right angles with each other in 
order to represent them. But if a greater extent of country is 
comprehended, it will be necessary to show the convergence of 
the meridians towards the poles, and the consequent diminution 
in the length of a degree on the higher and smaller*circles of 
latitude. The following are two practical methods for determin¬ 
ing these lines in both cases:— 

Suppose, as in the first of these cases, that A B C D (Fig. 41) 
is the boundary of a topographical map, upon which the meri¬ 
dians and parallels of latitude for every tenth minute are to be 
drawn. It is necessary, for this purpose, that the latitude and 
longitude of one point in the map should be known, and the 
direction of the true meridian passing through it determined. 
Suppose the longitude of the point a to be 4° 23' West, and its 
latitude 42° 18' North, its meridian being in the direction SN. 
Draw through a the line WE at right angles with the line SN. 
This will be the parallel of latitude passing through the point 
a. Since the meridian for every tenth minute is required, the 
first one West of a to be determined is that of 4° 30', which is 
seven minutes West of a. The first one to be determined on 
the right is that of 4° 20', which is three degrees East of a. The 
degrees of longitude expressing these distances must be con¬ 
verted into miles or yards, and then laid down upon the map 
according to the scale of distances. For this purpose the fol¬ 
lowing tables are used. Table 1 gives the different lengths of 
a degree of longitude, in terms of geographical miles, and table 
2 the same, in terms of statute miles:— 


TABLE I 


Showing the Length of a Degree of Longitude for every Degree 
of Latitude in Geographical Miles. 


Lat. 

Geographical 

Miles. 

Lat. 

Geographical 

Miles. 

Lat. 

Geographical 

Miles. 

Lat. 

<Geographical 
Miles. 

0 

60.00 

23 

55.23 

46 

41.68 

69 

21.51 

1 

59.96 

24 

64.81 

47 

41.00 

70 

20.52 

2 

59.94 

25 

64.38 

48 

40.15 

71 

19.54 

3 

59.92 

26 

54.00 

49 

39.36 

72 

18.55 

4 

59.86 

27 

53.44 

50 

38.57 

73 

17.64 

6 

69 .11 

28 

63.00 

51 

37.73 

74 

16.53 

6 

59.67 

29 

62.48 

52 

37.00 

75 

15.52 

7 

69.56 

30 

51.96 

53 

36.18 

76 

14.51 

8 

59.40 

31 

61.43 

54 

35.26 

77 

13.50 

9 

69.20 

32 

60.88 

55 

34.41 

78 

12.48 

10 

59.08 

33 

60.32 

56 

33.55 

79 

11.45 

11 

68.89 

34 

49.74 

67 

32.67 

80 

10.42 

12 

68.68 

35 

49.15 

58 

31.79 

81 

9.38 

13 

58.46 

36 

48.54 

59 

30.90 

82 

8.35 

14 

58.22 

37 

47.92 

60 

30.00 

83 

7.32 

15 

68.00 

38 

47.28 

61 

29.04 

84 

6.28 

16 

57.60 

39 

46.62 

62 

28.17 

85 

5.23 

11 

57.30 

40 

46.00 

63 

27.24 

86 

4.18 

18 

57.04 

41 

46.28 

64 

26.30 

87 

3.14 

19 

56.73 

42 

44.95 

65 

25.36 

88 

2.09 

20 

66,38 

43 

43.8 ’ 

66 

24.41 

89 

1.05 

21 

56.00 

44 

43.16 

67 

23.45 

90 

0.00 

22 

65.63 

45 

42.43 

68 

22.48 































53 


TABLE II. 

Showing the Length of a Degree of Longitude for every Degree 
of Latitude in English Statute Miles. 


Lat. 

Eng. Miles. 

0 

69.2000 

1 

69.1896 

2 

69.1578 

3 

69.1052 

4 

69.0312 

6 

68.9363 

6 

68.8208 

7 

68.6845 

8 

68.5267 

9 

68.3481 

10 

. 68.1489 

11 

67.9288 

12 

67.6880 

13 

67.4264 

14 

67.1448 

35 

66.8424 

16 

66.6192 

17 

66.1760 

18 

65.8134 

19 

65.4300 

20 

65.0265 

21 

64.6037 

22 

64.1609 


Lat. 

Eng. Miles. 

23 

63.6986 

24 

63.2177 

25 

62.7167 

26 

62.1963 

27 

61.6579 

28 

61.1001 

29 

60.5237 

30 

59.9293 

31 

59.3162 

32 

58.6851 

33 

58.0360 

34 

57.3696 

35 

56.6852 

36 

55.9842 

37 

55.2659 

38 

54.5303 

39 

53.7788 

40 

53.0100 

41 

52.2259 

42 

51.4253 

43 

50.6094 

44 

49.7783 

45 

48.9313 


Lat 

Eng. Miles. 

46 

48.0705 

47 

47.1944 

48 

46.3038 

49 

45.3994 

50 

44.4811 

51 

43.5489 

52 

42.6037 

53 

41.6453 

54 

40.6751 

55 

39.6917 

56 

38.6959 

57 

37.6891 

58 

36.6705 

59 

35.6408 

60 

34.6000 

61 

33.5489 

62 

32.4873 

63 

51.4161 

64 

30.3352 

65 

29.2453 

66 

28.4464 

67 

27.0385 

68 

25.9230 


Lat. 

Eng. Miles. 

69 

24.7992 

70 

23.6678 

71 

22.5294 

72 

21.3842 

73 

20.2320 

74 

19.0743 

75 

17.9103 

76 

16.7409 

77 

15.5665 

78 

14.3874 

79 

13.2041 

80 

12.0166 

81 

10.8250 

82 

9.6306 

83 

8.4334 

✓ 

84 

7.2335 

85 

6.0315 

86 

4.8274 

87 

3.6219 

88 

2.4151 ‘ 

89 

1.2075 

90 

0.0000 


If the scale of the survey is in statute miles, the length of a 
degree of longitude, in latitude 42°, will be found in Table II. 
This length is 51.4253. To find the distance from a to the first 
meridian on the left, which is seven minutes west of a , the 
following proportion is stated:— 

























54 


60' : 51.4253 : : 7' : the required distance, or. 5.9996 miles, 
which must be laid off from a to the left , and the meridian 
drawn through the point b, so found, parallel to NS. This 
will be longitude 4° 30'. To find the distance from a to the 
first meridian on the right, which is three degrees East of a , 
the following is the proportion to be stated :— 

60': 51.4253 :: 3': the required distance, or 2.5713 miles, which 
must be laid off from a to the right , and the meridian drawn 
as before through the point e so found. Other meridians are 
drawn parallel to NS, and at a distance from each other equal 
,to be. The parallels of latitude for every tenth minute are 
determined in the same way, for the parallel WE, being 42° 
18', the first oneNortli, or 42° 20', will be two degrees North of 
a , and the first one South, or 42° 10', will be eight degrees 
South of a. The following proportions may then be stated, 
noting that the length of every degree of latitude is sixty geo¬ 
graphical miles, or 69.2 statute miles:— 

60': 69.2 :: 2': the distance North of a, or 2.3 miles. 

60': 69.2 :: 8': the distance South of a , or 9.2 miles. 

Parallels of latitude are drawn through the points d and 
thus determined, and others parallel to them, and to WE, at a 
distance apart, equal to de. The above fractional parts of 
miles may be reduced to feet or yards by multiplying the 
decimal fraction by 5280 feet, or 1760 yards. 

In the second case, or where the survey covers a greater 
extent of surface than a hundred miles in length and breadth, 
the meridians must converge, and the parallels of latitude must 
conform to them. The following is a simple construction for 
this purpose, by which any portion of the earth’s surface, mea¬ 
sured by degrees, is represented by a similar portion of the 
map. Suppose the survey to lie between longitudes 1° East 
and 7° West, and 36° and 45° of North latitude, comprising 
eight degrees of longitude, and nine degrees of latitude. Let 
a {Fig. 42) be a point near the middle of the map, whose lati¬ 
tude is 40° 30' North, and whose longitude is 3° 20' West. It 
is required to draw meridians and parallels for every degree. 
Draw through a the vertical line N S for the meridian passing 
through that point. Find in miles (as before) the distances 
from a to latitude 41° North, and to latitude 40° North. These 
distances—taking 69.2 miles for a degree of latitude—are 34.6 


55 


miles above and below a. The points b and c are thus deter¬ 
mined, and are points on the parallels of 40° and 41° North 
latitude, and the distance b c is one degree of latitude, which 
must be laid off on the line N S, above and below b and c, 
until the whole extent of survey included by N S is marked off 
in degrees. Determine, as in the first case, the meridians 3° 
and 4° west, by laying off in miles the lengths of 20' to the 
right, and 40' to the left of 1ST and S, which are respectively 
situated in 45° and 36° of North latitude. These distances are, 
at N, by Table II, N <$=16.3437 miles, and N 6=32.6874 
miles, which are laid off on e d perpendicular to N S. At S, 
draw li g perpendicular to N S, and lay off from the table the 
distances 18.6614 miles to the right, and 37.3228 miles to the 
left. Then e d and h g will be each one degree of longitude, 
corresponding to the latitudes of 45° and 36° north. Draw the 
lines e h and d g , and through the points of division on N S 
draw lines perpendicular to N S, and they will divide e h and 
d g into degrees of latitude. The figure ehg d will then be a 
projection of nine degrees of latitude, and one degree of longi¬ 
tude. Other meridians may be thus determined :—With the 
diagonal distance e g or d h, as a radius, and from g and h as 
centres, describe the arcs i k and l m, and from d and e as 
centres, with the same radius, describe the arcs n o and jpg. 
Now, from the points d and 6 as centres, and with e d as a 
radius, draw two arcs intersecting i k at r, and l m at s, and from 
h and g as centres with h g as a radius, draw arcs intersecting 
n o at t, and jp g at u. Join r with t , and s with u , and divide 
right lines s u and r t into degrees of latitude, each equal to 
b c , and we shall have the meridians and parallels for 2° and 
5° west longitude. Determine the other meridians of the sur¬ 
vey in the same manner. The parallels of latitude may be 
composed of straight lines from one meridian to another, 
or, their points being determined on the meridians, a curve 
may be drawn through all those points having the same lati¬ 
tude. 





% 


56 


OF THE METHOD OF PROJECTING HORIZONTAL 
CFRYES, FROM THE LEVELS OF CERTAIN POINTS 
DETERMINED BY SURVEY. 

In surveying the ground, for the purpose of tracing upon its 
plan the horizontal curves, the points whose levels are deter¬ 
mined must be sufficiently numerous and close together, to ad¬ 
mit, without sensible error, of the supposition that the slope of 
the ground between them is uniform. The following method 
proceeds upon this supposition. Let A 

and C (Fig. 43), be two points on the pro- A„ == —- QuH -b 

file of the ground, and let the horizontal ' ——-ic 

distance (AB) between A and C be fifty feet. 

Let the difference of level between A and C, as determined by 
survey, be ten feet, C being the lowest point. It is required to 
find, upon A C, the points in which horizontal planes, drawn 
one foot apart, and commencing at A, will intersect A C. The 
following proportion will discover this :— 

As the total fall from A to C is 

To the horizontal distance A B from A to C, 

So is any partial fall from A towards C 

To its corresponding horizontal distance from A. 

Now A B is 50 feet, and the total fall from A to C is 10 feet, 
then for a partial fall of one foot we shall have 10 ft.: 50 ft.: 
1 ft.: 5 ft., or the horizontal distance from A to that point of 
A C, which is one foot below A : and by laying otf 5 feet from 
A towards C, we shall have the intersection of the one-foot 
plane with a line of the ground. Again, 10: 50 :: 2: 10, 
which gives ten feet from A, for the point of intersection of the 
two-foot plane with A C: and so on for the other planes. By 
marking out upon the ground squares, or triangles, whose sides 
are of equal and convenient length, determining the levels at 
all the intersections, and reducing all the levels so that they 
may be referred to one point (a horizontal plane drawn through 
such a point is called the plane of reference , and the levels so 
reduced are called references ), we can, by the above method, 
find, upon every line, the intersections of any horizontal 
planes. *• 

But the references, as obtained by the instrument, are 



57 


y 


scarcely ever expressed in whole numbers; and whereas it is 
desirable that the planes should be passed at whole numbers 
ot feet apart, the labor of stating a proportion to calculate 
every point becomes considerable. This is obviated by the 
following convenient mechanical method * by which the pro¬ 
portions, instead of being stated in figures, are presented in 
lines, by means of the properties of similar triangles. 

Let 1, 3, 9, 7 {Fig. 44), be a portion of ground, projected on 
a scale of 50 feet to an inch. It is 100 feet square, and is sub¬ 
divided into four squares, of 50 feet sides. Let the references 
of the points 1, 2, 3, &c., be respectively 8.10, 6.30, 7.25, &c., 
as indicated in the figure. These levels are expressed in feet, 
and are referred to a horizontal plane 2.5 feet above the point 
5; which is the highest point of the ground. It is required 
now to trace the intersections of horizontal planes, which shall 
be 8, 4, 5, 6, &c., feet below the plane of reference. Let us 
begin with the line 5, 6, Draw the line A B {Fig. 45), equal 
to the line 5, 6, or, according to the scale, fifty feet in length. 
Then let fall from A & B, two perpendiculars, A D & B C. 
Divide these perpendiculars into equal parts, say, each one 
tenth of A B, and join the opposite points of division, forming 
the ladder-like figure A B C D. Number the horizontal lines 
from B downwards, in quarters of unity, viz.: .25, .50, .75, 
1, 1.25, 1.50, &c., &c., so as to include the greatest number of 
feet the ground will probably descend, from station to station. 
In the present case 7.50 will suffice. Cut from a piece of stiff 
paper a narrow strip like E F, making the edge E F accurately 
straight. Fasten the line E F to the point B, by means of a 
fine needle, so as to conceal as little as possible of the corner at 
B, and the instrument is ready for use. Beginning at the cen¬ 
tral point, 5 (Fig. 44), it will be observed that the three-foot 
curve is .5, or half a foot below it; the four-foot curve is 1.5 
feet below it; the five-foot 2.5, and the six-foot 3.5 below it. 
The total fall from the point 5 to the point 6, is 6.50-2.50, or 4 
feet. Then the edge E F (Fig. 45), of the strip must be placed 
so that the line E F will be drawn from B to G, on the horizon¬ 
tal line marked 4, corresponding with the difference of level 


* Industrial Drawing. D. H. Mahan. 



58 


between stations 5 ' & 6. The strip must be secured in this 
position by a pin near E. Now from station 5, the first partial 
fall we wish to find, is from reference 2.50, to the three-foot 
curve, or .5 of a foot. 

The proportion is,—Total fall from sta. 5 to sta. 6, is to 

Distance from sta. 5 to sta. 6, as 
Partial fall, is to the distance required, 
or, by the instrument, A G, (or B H): IT G :: B i: i k. Hence, 
to find the horizontal distance corresponding to the partial fall 
of .5, we have only to measure on the horizontal marked .50, 
its length included between B H and E F {Fig. 45), and lay it 
off on the line 5, 6, {Fig. 44), from 5, towards 6. This will be 
a point of the three-foot curve. The next point, that of the 
four-foot curve, is 1.5 feet below station 5. Take the length of 
the line marked 1.50, included between B II & E F, and lay it 
off from 5, towards 6. The five-foot curve lies 2.5 feet below 
station 5 ; then we take the part of the line 2.5 included between 
B IT & E F, and lay it off as before. The six-foot curve being 
3.5 feet below, we measure and lay ofi‘ a similar part of the line 
marked 3.5. This finishes the division of the line between sta. 
5 to sta. 6, and gives points of the three, four, five, and six-foot 
curves; which must be marked (3) (4) (5) (6). Points of the 
curves on other lines are determined in the same manner. For 
example, from sta. 5 to sta. 4, the total fall is 6.50 feet. Set 
the edge E F, from B to L, on the line marked 6.50, and mea¬ 
sure and lay off successively from 5 towards 4, the parts in¬ 
cluded between E F & B M, of the lines marked .50,1.50, 2.50, 
3.50, 4.50, 5.50. The station 4, having a reference of 9 feet, is 
itself a point of the nine-foot curve. Find the points thus, 
upon every line of the figure, and draw the curves through the 
points so determined, taking care to give them their proper 
curvature from point to point. If the total fall from station to 
station is expressed in smaller fractions than .25, as for exam¬ 
ple from sta. 5 to sta. 2, where it is 3.80; then the line E F 
must be placed at a point between 3.75 and 4, but nearer to 
3.75 : or else the line B C may be divided and numbered, so as 
to show smaller fractions than J. 

In case the great irregularity of the ground should require 
intermediate levels and references, a distance must be laid off 
from B towards A, making N B equal to the horizontal distance 


59 


between these secondary points and the primary ones, and the 
line 1ST O drawn, and used for these, instead of the line A D, 
which latter is used for all the regular distances of the survey. 


OF THE METHOD OF PROJECTING HORIZONTAL 
CURVES OF THE GROUND UNDER WATER. 

In surveying a harbor, or any extensive body of water, flag- 
buoys are stationed at convenient points, and their positions, 
their distances from each other, and from some points on the 
shore at the water line, accurately surveyed and projected on 
the map. Soundings are taken along these connecting lines 
keeping the intervals of the soundings exactly equal between 
any two of the stations, though they may vary for different 
lines. In order to determine the curves of the bottom, it .is 
necessary to distribute the soundings of each line, equally 
throughout its length. Suppose (Fig. 34, “ soundings”) the 
line between the two buoys to be one of the projected lines, 
and that its length is 630 feet. The number of recorded 
soundings corresponding to that line is 22, including the 
soundings at the buoys. This will give 21 intervals between 
the soundings. Then the line must be divided into 21 equal 
parts, of 30 feet each. Mark the points of division on the 
line, and write opposite to each point its corresponding sound¬ 
ing. The points of any desired curve may now be found :—for 
example, the six-foot and nine-foot curves will pass through 
the points 6 and 9, the twelve-foot and fifteen-foot curves will 
pass midway between the points 111 and 12§, and 14^ and 
155 , respectively. In the same manner other lines of sound¬ 
ings may be divided, and points of the curves determined. 
Through all the points so found, the curves are drawn, after 
which they are numbered (as in the figure) at a sufficient num¬ 
ber of places. 

The following easy method of dividing a line into any 
number of equal parts, will save the labor of measuring, or 
dividing by trial. Cut a strip of drawing paper, the edge 
A B of which (Fig. 45£) is graduated in equal divisions. If 
it be required to divide the line c d into nineteen equal parts, 
place the strip so that its edge A B shall make a convenient 


# 


60 


/ 


Fig . 45|. 



angle with c d , and so that the zero of its graduation shall 
coincide with the point c. Secure the strip in this position. 
Now join the point d with the point 19 of the scale A B, 
and draw, parallel to 19 d, lines through all the inferior 
points of the graduation, and these lines will cut c d into 
nineteen equal parts. 


PROBLEMS CONNECTED WITH THE REDUCTION, EN¬ 
LARGING, AND COPYING OF MAPS OR PLANS. 

Problem I. 

To Construct a Square that shall be a Multiple of any given 

Square. 

Let A B C D {Fig. 46) be the given square, and let it be 
required to construct a square that shall contain 2, 3, 4, 
&c., times its surface. Draw the 
diagonal B D, and make B a equal 
to B D—then the square described Fig.^6 
upon B a , will be double the square 
A B C D. Lay oif A E, equal to c 
B &, and draw B E, then the square 
described upon B E, or B 5, will be 
three times the square A B C D. 

In the same manner, lay off A F b 
equal to B b , and the square described upon B F, or B c , will 
be four times the square A B C D, and so for any multiple of 
the square A B C D. 









61 


Problem II. 


To Construct a Square that shall be equal to 4, c&c., of 

any given Square. 


Let AB CD (Fig. 47) be tbe given 
square. On A B, as a diameter, de¬ 
scribe tbe semi-circle A H B, and 
erect, at tlie centre E,the perpendicular 
E H. Draw B H, and it will be tbe 
side of a square equal to one-balf of 
A B C D. Lay off F B, equal to one- 
fourth of A B, and erect tbe perpen¬ 
dicular F I, then tbe square described 
upon I B will be equal to one-fourth 
of A B C D. In tbe same manner, a 
square may be constructed, equal to 
any part of A B 0 D. 



Problem III. 


To Construct a Square that shall be in any Proportion to a 

given Square. 


Let A B C D (Fig. 48) be the 
given square. It is required to con¬ 
struct a square which shall be to 
A B C D as 2 is to 5. Upon the side 
A B as a diameter, describe the semi¬ 
circle A G B, and divide the line 
A B into five equal parts. At the 
second point of division, erect the 
perpendicular F G, and join A G— 
the square described upon A G will 
be to the given square A B C D as 2 
is to 5. 















62 


Problem IV. 


To Construct upon a given Base , a Rectangle , which shall be 

similar to a given Rectangle. 

Let A E P G be the given rectangle. It is required tc 
construct upon the base 
A B, one that shall be 
similar to A E F B. Pro¬ 
long A E, and lay off the 
given base from A to B. 

Draw the diagonal A G, 
and prolong it indefinitely. 

Erect a perpendicular to 
A B, at B, and at the 
point D, where it inter¬ 
sects the prolonged diago- A E 

nal, let fall D C, perpendicular to A F produced. Then 
A B C D will be similar to A E F G. All rectangles having 
their diagonals in the same line are similar. 































































































































































































































Urnfhl o/ zo/ic Zyds.6 curves r/t / xn/tr 


] »V hrtrjt r n fhr h o ri zo nio / Sysir. m. 





















































































































































































w t Heal rrr\ 



I itli.of J.Bier.’•* a v 














































































































































































Lift.J. Bien.UVo^St RY. 







































































































































































































































ibo^ 


Scale.\ 5 2 So 


zortr 0 fi 






■1! 


Fig IS 

ihoo ft 


\\\ 


\V'N 


AWW 


\N^\\\\\\\ O- 


ill ;v 


Firj. 2 4. bu<. 





/■ 

uj. 28. 


a 

c d> 

<&. 

Q>_ 

<5> 


■ % 

% 

% 


% 

% 


9 

<& 

© 

9 

Q> 

% 

% 

% 

% 

% 

% 

q 

% 

Q> 

% 

Q> 

& 

■Q 

% 


'% 

% 

% 

r j> 

Q, 

<55 

Q> 

QS 

© 

% 

% 

%, 

% 

% 

%. 


9 

0/ 

Q> 

Q. 

Q 

\ 

% 

\ 

% 

%. 

% 

<3 


Q> 


© 

ig 

% 

% 

% 

% 

•% 

% 

% 


Fig. 20. 
a 



& 

% 


Fig. 20. 


Fig. •>/ 


Fig. Ft). 





u , 

‘ r ?i t 

| § * f4ti 


£ til 

A ' 


i H 

! t i t i 
t :'t 




*v; 1 ? 




big 2 7. bis 

F~, cFf-F i j.-r), 

Sj° J 


Fig. Si 


Fig. 32. 


'///// 
/• //* 






/ /////. 


s 


\V\\-\. . ' - 


/ r 


\ v > . s \ ' v S \'%,'///// //// .- 
\ v. : v v \- ; siy/////, , v> : , -/ >• . 


Yf 




/ 


\ 

\ \ 


\ N 


J 


r ,.v J Bie:. r.4 Veser Si 1 




























































































Fig. 28. 


© 

• % 

l 3> 

% 

\ 

H- 

<5> «® 

% % 

Q> 

% 

a 

% 

9 

% 

\ 

O 

% 

& Q> 

% % 

© 

% 

© 

% 

Ss 

% 

Q 

o 

k 

<5> G> 

% % 

Q> 

% 

% 

Q. 

% 

<3L 

% 

%. 

a © 

% % 

o 

% 

a 

% 

% 

© 

% 

Q> 

% 

Qj. © 

%. % 

a 

% 

<3 

m 

a 

% 

G> 

% 

Qti 

•K 

© 

% % 

8> 

% 


Fig. SO. 

f£ 1 .£ - - t'- * i t i 

<* ft, fi$ .!> 

*■ •** .-.4 


Fig 20- 


Fig. •>/ 


Fig 32 


r J Bj er. ?.4 V«s«<r ik i' \ 





































































































































































































Fi<). 3$. 

■Scale o/' di.stances iooo 


400 


son 


_ 2 00 


300 


Fig. 40. 

dealt of (vnstructivn 24 luc ] t f a / n ,,/ v 



Lull J Biftj! K NY 












































































































































































































































































































CTOBZHNr WILIER- & S OIST, 

535 Broadway, New York, 


PUBLISH -AJSTD OFFER FOR SALE: 

Free by mail when paid for in advance. 


; *riculture, etc. — agricultural 

■ CHEMISTRY. By Justus Liebig. 1 vol., 12mo, 
cloth,.$1 00 

AGRICULTURAL CHEMISTRY. Principles of. 
With special reference to late researches in Eng¬ 
land. By Justus Liebig. 1 vol., 12mo, cloth, 75 

AGRICULTURE. Letters on Modern. By 
Justus Liebig. 1 vol., 12mo, cloth, . . 1 00 

FLAX COTTON. Directions for the Cultivation 
of Flax and Preparation of Flax Cotton. By 
Chev. Claussen,.25 

FRUITS AND FRUIT TREES OF AMERICA. 
Culture, Propagation, and Management. By 
A. J. Downing. Revised by Charles Downing. 
1 vol., thick 12mo, plates,.3 00 

GARDENING FOR LADIES AND COMPAN¬ 
ION TO THE FLOWER GARDEN. By Mrs. 
Loudon. Edited by A. J. Downing. 1 vol., 
12mo, cloth, .2 00 

HORTICULTURE. Lind ley’s Horticulture. 
With additions by A. J. Downing. 1 vol., 
I2mo, ..2 00 

LANDSCAPE GARDENING. How to Lay Out 
a Garden from a quarter of an acre to one hundred 
acres in extent. By Edward Kemp. 1 vol., 
12mo, cloth, numerous plates, .... 2 00 

ROSE (THE). Its History, Poetry, Culture, and 
Classification. By S. B. Parson. 1 vol.!2mo, 1 25 

'cliitecture, etc .—architecture and 

PAINTING. Lectures on. By John Ruskin. 
1 vol., 12mo, plates, cloth,.1 50 

ARCHITECTS—LECTURES BEFORE THE 
SOCIETY OF. By John Ruskin. Pamphlet, 15 

CARPENTRY. THE AMERICAN HOUSE 
CARPENTER. A Treatise upon Architecture, 
Cornices and Mouldings, Framing, Doors, Win¬ 
dows, and Stairs. By R. G. Hatfield. 1 vol., 

8vo., numerous plates, cloth,.3 50 

CARPENTER AND JOINER’S HANDBOOK. 
A useful book for Carpenters and Wood Workers. 
By H. W. Holly. 18mo, cloth,.75 

COTTAGE RESIDENCES. A Series of Designs 
for Rural Cottages and Cottage Villas, with Gar¬ 
dens and Grounds. By A. J. Downing. 1 vol., 
8vo., plates,.3 00 

( HINTS TO YOUNG ARCHITECTS, AND TO 
PERSONS ABOUT BUILDING IN THE 
COUNTRY. Edited by A. J. Downing. 1vol., 
8vo, ..2 00 

SEVEN LAMPS OF ARCHITECTURE. By 
John Ruskin, author of “Modern Painters.” 
1 vol., 12mo, plates, cloth,.1 75 

isaying. — a treatise on the assay¬ 
ing OF LEAD, COPPER, SILVER, GOLD, 
AND MERCURY. By Bodemann and Kerl. 
Translated by W. A. Goodyear. 1 vol., 12mo, 
cloth,.3 50 

stronomy. — a treatise on astron¬ 
omy. Designed for Colleges, High Schools, 
and Academies. By Prof. W. A. Norton. Anew 
edition, entirely revised, largely re-written, and 
brought up to present time. 1 vol., 8vo 3 50 


Blowpipe Analysis. — a treatise on 

THE. By Prof. C. J. Brush. (In preparation). 

Bookkeeping and Accountantship. 

ELEMENTARY AND PRACTICAL. In two 
parts, with a Key for Teachers. By Thomas 
Jones, accountant and teacher. 1 vol., 8vo, 
cloth,.$2 50 

“ SCHOOL EDITION. By Thomas Jones. 1 vol., 
8vo, half roan,.1 50 

“ SET OF BLANKS. In 6 parts. By Thomas 
Jones,.1 50 

“ DOUBLE ENTRY; Results obtained from Single 
Entry; Equation of Payments, etc. By Thomas 
Jones. 1 vol., thin 8vo,. 75 

Chemistry.— an elementary manual 

OF QUALITATIVE CHEMICAL ANALYSIS. 
By Prof. Maurice Perkins. 1 vol., 12mo, 
cloth,.1 00 

“ A MANUAL OF QUALITATIVE CHEMICAL 
ANALYSIS. By C. R. Freeenius. Edited by 

Prof. Johnson. 1 vol., 8vo, cloth, ... 4 50 

“ A SYSTEM OF INSTRUCTION IN QUANTI¬ 
TATIVE CHEMICAL ANALYSIS. By Dr. C. R. 
Fresenius. 1 vol., 8vo, cloth, .... 

“ ELEMENTS OF CHEMISTRY—THEORETI¬ 
CAL AND PRACTICAL. By Wm. Allen Miller, 
M. D., LL.D. PART I.— Chemical Physics. 
1 vol., 8vo,.4 50 

“ PART II. — Inorganic Chemistry. 1 vol., 

8vo,. 

“ PART III. — Organic Chemistry. 1 vol., 
8vo,. 

Clock and Watchmaker.— new and 

COMPLETE CLOCK AND WATCHMAKER’S 
MANUAL of French, Swiss, and English Clocks 
and Watches, Cleaning and Repairing, etc., etc. 
By M. L. Booth. 1 vol, 12mo, plates, ..200 

Drawing, etc. — coe’s drawing cards. 

Containing the latest Drawings of B. II. Coe. 
In five series, as follows, in neat covers: 

1. 

« DRAWING FOR LITTLE FOLKS. . . 37* 

2 . 

« FIRST STUDIES IN DRAWING. Complete 
in 3 numbers of 18 Cards each. Per No. . 37* 

3. 

« COTTAGES, AND INTRODUCTION TO 
LANDSCAPE. 4 numbers of 18 Cards each. 


Per No.37* 

4. 

“ EASY LESSONS IN LANDSCAPE. 4 num¬ 
bers of 10 Cards each. Per No.37* 

5. 


“ HEADS, ANIMALS, AND FIGURES. 3 num¬ 
bers of 10 Cards each. Per No.37* 

« COPY BOOKS. Of Good Quality and Proper 
Size,.27* 

































2 


JOHN WILEY & SON’S TRADE LIST 


Descriptive Geomety, Drawing, 

etC.— DESCRIPTIVE GEOMETRY. Ap¬ 
plied to the Drawing of Fortifications and Stone 
Cutting. By Prof. D. H. Mahan. 1 vol., Svo, 
plates,.$1 50 

“ INDUSTRIAL DRAWING. Comprising Use 
of Instruments; Construction of Figures; Pro¬ 
jections; Elements of Mechanism ; Topographical 
Drawing : etc. With numerous plates. By Prof. 
D. H. Mahan. 1 vol., Svo, cloth, ... 2 50 

“ ELEMENTS OF DRAWING. 1 vol. I2mo, plates, 
cloth. By John Ruskin,.1 00 

“ TOPOGRAPHICAL DRAWING. A Manual for 
Engineers and others. By Prof. R. S. Smith. 
1 vol., 8vo, numerous plates, cloth, ... 2 00 

« DESCRIPTIVE GEOMETRY. General Prob¬ 
lems from the Orthographic Projections of De¬ 
scriptive Geometry, etc. By Prof. S. E. Warren. 
1 vol., Svo, plates,.4 00 

“ DRAFTING INSTRUMENTS. A Manual of 
Drafting Instruments. By Prof. S. E. Warren. 
1 vol., 12mo, plates, cloth, .1 25 

“ GEOMETRICAL DRAWING. Manual of 
Elementary Geometrical Drawing. By Prof. S. E. 
Warren. 1 vol., 12mo, plates, .... 1 50 

“ ELEMENTARY PLANE PROBLEMS. This 
work is designed to embrace, in a cheap and por¬ 
table form, a fuller collection of Plane Problems 
than can elsewhere be found in a separate work ; 
and is intended for a text book as well as for 
general use. By Prof. S. Edward Warren. 1 vol., 

12mo, 1 25 

« SHADES AND SHADOWS. General Problems 
of Shades and Shadows, formed both by Parallel 
and by Radial Rays, and shown both in Common 
and in Isometrical Projection ; together with the 
Theory of Shading. By Prof. S. Edward Warren. 
1 vol., Svo, plates,.3 50 

u OIL PAINTING. Hand Book of Oil Painting. 
Adapted for a text book and for self instruction. 

1 vol., 12mo, cloth,.2 00 

“ PERSPECTIVE. ELEMENTS OF PERSPEC¬ 
TIVE. Arranged for the use of schools. By 
John Ruskip. 1 vol., 12mo, cloth, ... 1 00 

“ PERSPECTIVE. MANUAL OF LINEAR 
PERSPECTIVE. Form, Shade, Shadow, and 
Reflection. By Prof. R. S. Smith. 1 vol., Svo, 
plates, cloth,.2 00 

«• PERSPECTIVE. MANUAL OF LINEAR 
PERSPECTIVE. By Prof. S. E. Warren. 1 vol., 

12mo, cloth,.1 00 

Dyeing and Calico Printing. —a 

PRACTICAL TREATISB. By an experienced 
Dyer. With a Supplement by Robert Macfarlane. 

1 vol., Svo, numerous plates,.5 00 

Electricity and Magnetism.— By 

William Allen Miller, M. D., LL.D. 1 vol., Svo, 
cloth,.2 50 

Electro Metallurgy. — elements of. 

By Smee. 1 vol., 12mo,. 

Engineering, etc.—A merican engi¬ 
neering. Illustrated by large detailed en¬ 
gravings. In 26 numbers, folio. By G. Weis- 

senborn,. 36 00 

do. do. 2 vols., half morocco, . . 42 00 

“ LOCOMOTIVE ENGINEERING, AND THE 
MECHANISM OF RAILWAYS. A Treatise on 
the Principles and Construction of the Locomo¬ 
tive Engine, Railway Carriages, and Railway 
Plans. Illustrated with sixty large engravings 
and numerous woodcuts. By Zerah Colburn, C. E. 
Complete in Two Parts. Part I., 1 vol., 4to, 
cloth.]1 00 






Engineering, etc.— civil engini! 

ING. ELEMENTARY COURSE OF. By .? 
D. H. Mahan, of West Point. 1 vol., 8vo a 
numerous cuts,.£1 




MECHANICAL PRINCIPLES OF E 3 
NEERING AND ARCHITECTURE. By I j 
ley. Edited, with additions, by Prof. D. H.M i 
1 vol., 8vo,. 


ti 


MOLESWORTH’S POCKET BOOK OF E 3 
NEERING FORMULAE,. 


Hebrew Grammar, etc. — a Gift 

MAR OF THE HEBREW LANGUAGE. 1 
copious Appendixes. By Prof. W. H. Green, i 
Svo, cloth,. 

AN ELEMENTARY HEBREW GRAMM 
With Tables, Reading Exercises, and Vo t 
lary. By Prof. W. II. Green. 1 vol., * 
cloth, . 


u 


HEBREW CHRESTOMATHY; or, Lesso 
Reading and Writing Hebrew. 1 vol., 1 
cloth,.11 


I 


Horse Railways. — street or hcd 

POWER RAILWAYS. By A. Easton, 

1 vol., 12mo, plates, cloth,. ft 


A 


U 


Iron, etc. —cast and wrought. a pp i i 

building purposes. By William Fairbairn. It 
Svo, cloth,. 

FRENCH. HISTORY AND PROGRESS*:- 
THE IRON TRADE—From 1621 to 1S57, ij 
United States. 1 vol., Svo, cloth, . . . 

TRURAN, W., ON THE IRON MANUl 
TURES OF GREAT BRITAIN. 1 vol., 1 
(London edition), plates,.mi; 


U 


Lead Pipe. — collection of repci f 

AND OPINIONS OF CHEMISTS—On thip 
of Lead Pipes for service pipe in the distrili 
of Water. By J. P. Kirkwood, C. E. 1 vol. i 
cloth, . 


Marine Boilers. — treatise 

MARINE BOILERS OF THE 
STATES. 1 vol., Svo, cloth, . . . 


ON E 


a: 


UNI I 


Medical, etc. — BRONCHITIS. ATreati 


c. 

Ai 


Diseases of the Air Passages, and those t 
tions of the Throat called Bronchitis, etc ; 
By Horace Green, M. D. 1 vol., Svo, plates, 


CONSUMPTION. A Practical Treatise on i 
monary Tuberculosis; embracing its Hbl 
Pathology, and Treatment. By Horace G t 
M. D. 1 vol., Svo, cold plates, cloth, . . 

CROUP. The Pathology of Croup, with re; r 
on its treatment by Topical Medication. 3 
Horace Green, M. D. 1vol., Svo, . . . 

FAVORITE PRESCRIPTIONS. Seleo 
from Favorite Prescriptions of living Ame J 
Practitioners. By Horace Green, M.D., IJ • • 
1 vol., Svo,. 

LARYNX. The Surgical Treatment ol t 
Polypi of the Larynx, etc. By Horace Gt 
M. D. 1 vol., Svo,. 

HINTS TO MOTHERS for the Managemcl Cl 
Health during the period of Pregnancy, a; |0I 
the Lying-in-room, etc., etc. By Dr. Tbtt 
Bull. 1 vol., 12mo,. 

HYDROPATHY. GUIDE TO HYDROPAM A 


(( 


By Cla 


f 11 ■' 

I 


or Every Man his own Doctor. 

1 vol., 12mo, cloth, 

HYDROPATHY. THE THEORY’AND P i 
TICE OF HYDROPATHY. Intended for po 
use. By II. Francke. 1 vol., 12mo, cloth, 


.1 C( 

Et 




































3 


JOHN WILEY & SON’S TRADE LIST. 


dical, etc. — hydropathy, results I Miscellaneous.— DECIMAL SYSTEM 

OF HYDROPATHY ; or, Constipation not aDis- Extension to Weights and Measures in h 

» .v T. _with the National Currency. By J. H. 


ease of the Bowels—Indigestion not a Disease of 
the Stomach. By Dr. Edward Johnson. 1vol., 

12mo, cloth,.^l 00 

HEALTH OF WOMEN at the Critical Periods 


of Life. By J. E. Tilt, M.D. 1 vol 

cloth, . 

MICROSCOPICAL DIAGNOSIS. 


18mo, 

50 


ON. By 
cloth, . 


Gustaf Yon Duben. 


TREATISE 
1 vol., 8vo, 
. . . 1 00 


R D 


litary, etc. — advanced ouAa., 

OUTPOST, AND DETACHMENT SERVICE. 
By Prof. D. II. Mahan. 1 vol., lSrno, plates, 1 25 

FIELD FORTIFICATIONS. A Treatise on, 
with numerous illustrations. By Prof. D. H. 
Mahan. Enlarged, 1 vol., 8vo, cloth, . . 3 50 

PERMANENT FORTIFICATIONS. A Treatise 
on, with plates. By Prot. D. 11. Mahan. 1 ' ol., 

8vo, cloth,.^ 

FORTIFICATIONS AND STONE CUTTING. 
Descriptive Geometry applied to the Drawing of. 
By Prof. D. II. Mahan. 1 vol., 8vo, plates, 

cloth, . 


1 50 


inine and Metallurgy of Gold 

AND SILVER. By J. A. Phillips, Mining En- 


AND SILVER. By 
gineer. 1 vol, Svo, nearly read^. 


acliinist. —the boston machinist 

for the Apprentice and advanced Machinist; 
showing how to make and use every tool 
Treatise on Screw and Gear 


« 


a 


With 
Cutting. By 


Walter Fitzgerald. 1 vol., ISmo, cloth, 


75 


The 

armony 

with the National Currency. By J. H. Felton. 

1 vol., ... 

HISTORY AND LIFE of Rev. Dr. John Tauler, 
of Strasbourg. With Preface by Rev. Charles 

Kingsley. 1 vol., 12mo,.* 

INFIDELITY. The Causes and Consequences 
of—(Perversion: A Tale of the Times), by Rev. 
W. J. Conybeare. 1 vol., 12mo, cloth, . 1 00 

KNITTING, NETTING, AND CROCHET. By 
Mrs. Gangain and Gore. Svo, plates, . . 

LEILA ADA: The Jewish Convert. Including 
her Diary. By O. T. Heighway. 1 vol., 18mo, 

cloth,. 1 UU 

LEILA ADA: Relatives of. By 0. T. Heigh¬ 
way. 1 vol., 18mo, cloth,. ?5 

NEW TALE OF A TUB. An Adventure in 
Verse. By T. W. N. Bailey. With plates. 1vol., 

12mo, . 60 

NOTHING TO YOU; or, Mind your own Busi¬ 
ness. An answer to ‘‘Nothing to Wear.’ Plates, 

cloth,. 75 

PARIS SOCIAL. A Sketch of Every-day Life 

in the French Metropolis. By Col. R. H. Addi¬ 
son. 1 vol., 18mo, cloth, plates, • • • 1 5U 

PENTATEUCH VINDICATED from the As¬ 
persions of Bishop Colenso. By Prof. W. H. 
Green, D.D. 1 vol., 12mo, cloth, ... 1 25 

PROVERBIAL PHILOSOPHY. A Book of 
Thoughts and Arguments, including 1000 lines. 
By M. F. Tupper. 1 vol., 12mo, cloth, . 1 25 

POCKET BIBLE—Story of. 1 vol., 12mo, 

plates, cloth,. 

WALTON AND COTTON. COMPLETE 
ANGLER; or, The Contemplative Man’s Recrea¬ 
tion. Edited by Dr. Bethune. 1 vol., 
plates, cloth extra,. 


12mo, 
3 00 


Lscellaneous.— ART OF MEMORY. Pheno 
Mnemotechny; or, the Art of Memory. By 


Being 


Bv Francis F. Gourand. 

.... 2 00 


of English Language. 

1 vol., Svo, . ... 

AMERICAN ANTIQUITIES and Researches in 
the Origin and History of the Red Race. By 
A W. Bradford. 1 vol., Svo, . . . . 1 5U 

CATALOGUE OF AMERICAN BOOKS. The 
American Catalogue of Books, from January 186 
to January 1S66. Compiled by James Kelly. 

1 vol., Svo, net cash, . 

CARLYLE’S HEROES AND HERO WORSHIP, 
and the Heroic in History. By Thomas Carlyle 
1 vol., 12mo, cloth,. 

CHEEVER. CAPITAL PU J I 5* IMEXT ' £ 
of. By Rev. George B. Cheever, D. D. 

... 50 


United States; their Nature, Position, Aims, and 

.. 4 


UNIFORM IN SIZE AND STYLE. 

Raskin’s Works— modern painters. 

5 vols., tinted paper, bevelled boards, plates, in 

box,. 

half calf,.21 00 

without plates, white paper, 9 00 

17 50 


do. 

do. 


it 






Defence 
Cloth, . 

CHEEVER. HILL DIFFICULTY, and other 
Miscellanies. By Rev. George B. Cheever, D. D. 

1 vol., 12mo, cloth,. 

CHEEVER. JOURNAL OF THE PILGRIMS 
AT PLYMOUTH ROCK. By Geo. B. Cheever, 
D.D. 1 vol., 12mo, cloth,. 1 

CHEEVER. WANDERINGS OF A PILGRIM 
IN THE ALPS. By George B. Cheever, D. D. 

1 vol., 12mo, cloth,. 

CHEEVER. WANDERINGS OF THE RIVER 
OF THE WATER OF LIFE. By Rev. Dr. Geo. 
B. Cheever. 1 vol., 12mo, cloth, . . 

CHINESE EMPIRE. The Middle Kingdom. 
A Survey of the Geography, Government, E ^ca- 
Con Social Life, Arts, and Religion of the 
Ohiiefe Empire. By S. Welles Williams. 2 ™ls., 

12mo, plates,. 

CORTES DESPATCHES. Addressed 
Emperor Charles 5th. 1 vol., 12mo, . 


ft 


do. 
do. 

do. do. do. half calf, 

STONES OF VENICE. 3 vols., on tinted paper 

bevelled boards, in box,. 7 00 

do. do. white paper, 3 vols., cloth, . 5 00 

do. do. * half calf,. 12 00 

MISCELLANEOUS WORKS. Including “Seven 
Lamps of Architecture;” “Lectures on Architec¬ 
ture and Painting;" “Two Paths;” “Elements 
Drawing;” “Elements of Perspective; 


of 


to the 
1 50 


“ Political Economy of Art;” “ Pre-Raphaelitism; 
“Construction of Sheep-folds;” ‘ king of the 
Golden River;” “ Sesame and Lilies; ‘ Lecture 

before Society of Architects £’ “ The f w-Jq OHv^” 
Dust« Unto this Last;” “ Crown of Wild Olive. 

5 vols., on tinted paper, bevelled boards^ in 

box,. 

5 vols., half calf, 


« 


« 


do. do. 

SEVEN LAMPS OF ARCHITECTURE. 

12mo, cloth, . 

do. do. 1 vol., 12mo, plates, cloth, 

LECTURES ON ARCHITECTURE 
PAINTING. 1 vol., 12mo, cloth, plates, 
TWO PATHS. Being Lectures on Art. 
12mo, cloth, plates,. 


21 00 

1 vol., 
1 25 

1 75 
AND 
1 50 

1 vol., 
1 25 





































JOHN WILEY & SON’S TRADE LIST. 


Ruskin’s Works. — elements of 

DRAWING. 1 vol., 12mo, cloth, plates, $1 00 

“ ELEMENTS OF PERSPECTIVE. 1 vol. 12mo, 
cloth,.1 00 

“ POLITICAL ECONOMY OF ART. 1 vol., 
12mo,.1 00 

« PRE-RAPIIAELITISM—Construction of Sheep- 
folds—King of the GoldeD River. 1 vol., 12mo, 
cloth, .1 00 

i “ SESAME AND LILIES. Two Lectures on 
", Books and Women. 1 vol., 12ino, cloth, 1 00 

■ ! “ LECTURE BEFORE SOCIETY OF ARCHI¬ 
TECTS, . . . *. 15 

“ THE ETHICS OF THE DUST. Ten Lectures 
to Little Housewives, etc. 1 vol., 12mo, . 1 25 

“ UNTO THIS LAST. Four Essays on the First 
V Principles of Political Economy. 1 vol., 12mo, 

cloth,.1 00 

« THE CROWN OF WILD OLIVE. Three Lec¬ 
tures on Work, Traffic, and War. 1 vol., 12mo, 
cloth,.1 00 

« MISCELLANEOUS WORKS. Yol. 5, contain¬ 
ing “Ethics of the Dust,” and “Unto this Last.” 
On tinted paper, uniform with “Works.” . 2 50 
“ COMPLETE WORKS. On tinted paper, and in 
bevelled boards, including “ Crown of Wild 
Olive.” 13 vols. in three boxes, . . . 35 00 

Saw Filing. — the art of saw filing 

Scientifically treated and explained. "With di¬ 
rections for putting in order all kinds of Saws, 
By II. W. Holly. 18mo, cloth, .... 75 

Screw Propeller. —a treatise on the 

SCREW PROPELLER, Screw Vessels, and Screw 
Engines. Illustrated by numerous engravings 
and wood-cuts. By John Bourne, C. E. Com¬ 
plete in two parts. Part I., 1 vol., 4to, . 15 00 

Ship Building.— THEORETICAL AND 
PRACTICAL. Consisting of the Hydraulics of 
Ship Building; or, Bouyancy, Stability, Speed, 
and Design—The Geometry of Ship Building; or, 
Modelling, Drawing, and Laying Off—Strength 
of Materials as applied to Ship Building—Masts, 
Sails, and Rigging—Marine Steam Engineering— 
Ship Building for Purposes of War. By Isaac 
Watts, C. B.; W. J. M. Rankine, C. E.; Fred’k Iv. 
Barnes ; James Robert Napier, etc. Illustrated 
with numerous fine engravings and wood-cuts. 
1 vol., folio, cloth,.. 40 00 

do. do. half russia,.. 45 00 

Ventilation. — ventilation in Ameri¬ 
can DWELLINGS. Illustrated by numerous 
plates. By Dr. D. B. Reid. 1 vol., 12mo, 1 50 


BEAUTIPUL PRESENTATION VOLUMES. 


Printed on tinted paper, and elegantly bound in crape 
cloth, extra, bevelled boards, gilt head. 


RUSKIN’S BEAUTIES; or, The True and the Beautiful 
in Nature, Morals, and Religion. 1 vol. 12mo, $2 50 

RUSKIN’S PRECIOUS THOUGHTS — Moral and 
Religious. 1 vol. 12mo,.2 00 

RUSKIN’S SESAME AND LILIES. lvol.l2mo, 1 50 

RUSKIN’S ETHICS OF THE DUST. 12mo, 1 75 

RUSKIN’S CROWN OF WILD OLIVES. 12mo, 1 50 

WALTON AND COTTON’S COMPLETE ANGLER. 
Edited by Rev. Dr. Bethune. Plates, cloth, . 3 00 

THE VOICES OF THE YEAR; or, The Poet’s 
Kalendar. Containing the choicest Pastorals in our 
Language, for every month in the Year. 1 vol., 8vo, 
plates, full gilt, cloth, extra,.4 00 


The Following English Publication 


will be sold from this date at same discount an < 
same terms as our own Publications. Full 


Catalogues gratis. 

Bagster’s & Son’s Bibles, etc., eti 
Alford’s (H., D.D.) Greek Tes- 

tament. 4 vols., 8vo, cloth, .... $51 

Wordsworth (Chr., D.D.) Greek 

Testament. 2 vols., royal 8vo,.4l 

The Publications of the London 

Tract Society. 

Murray’s Hand Book for Travelhs 
Black’s “ “ “ 

The Picture Reward Cards of 


Campbell & Tadhope, Tract Society, and Gall & 
Ingles. Consisting of over 100 varieties. 

The Sunday at Home. 

A Family Magazine for Sabbath Reading. Is¬ 
sued in Monthly Parts. Royal 8vo, numerous 
wood gravings, and colored plates ; per year, . 
The back vols., from 1853-61, cloth, each, . . 

The back vols., for years 1862, ’3, ’4, ’5, and ’6, 
enlarged size,. 

The Leisure Hour. 

A Family Journal of Instruction and Recreation, 
with numerous wood engravings and colored 
plates. Royal Svo, in Monthly Parts; per year, 
Back vols., from 1852-61, cloth, each, . . . 

do. do 1862-66, each,. 

The Child’s Companion. 

With numerous wood engravings and colored 
plates. In Monthly Parts; per year, . . . 

Back vols., from 1861-66, cloth, each, . . . 


1 

( 


J. W. & SON are Agents for the Sale of 

The Beautiful Cambridge Bibles, 

and offer the same on the most liberal terms. 
Catalogues gratis. 


Beautiful English Juveniles, 

on same terms as our own Publications. 


The Nursery Rhymes, Old & Nev 

1 vol., sq. 16mo, beautifully bound, illustrated, !| 

Ward & Lock’s Painted Toy Book. 

Printed in colors, very beautiful—“ The House 
that Jack Built,” “ Death of Cock Robin,” 
“Comical Cat,” “Mother Hubbard,” “Jenny 
Wren,” “New Picture Alphabet,” “Nursery 
Rhymes,” “Greedy Ben,” “Naughty Pup¬ 


pies,” “ Little Pussy Cats.” Per doz. 


6'I 


The Diverting History of John 

Gilpin. Illustrated by C. A. Doyle. Colored 
plates. Per doz.6 ( 

Beautiful Juvenile Tales. 


Elegantly printed in colors, 4to, fancy covers— 
“Children in the Wood,” “Little Red Riding 
Hood,” “Jack and the Bean Stalk,” “Jack the 
Giant Killer.” Per doz.4 C 


Nursery Rhymes, Old & New. 

10 different varieties, in fancy covers, per doz. 

Picture ABC and Primer. 


3 I 


With numerous illustrations, fancy covers. 
Per doz. 


4 ] 


'0 


34 80 





















































































o ■* o 

2»’* -b y* : 
fs o> \ 

.9* .' ••- *> V s *•• • ’ 

/ .W/k; ^ > • 

0* . 1 ' * * o 

c u * o 



v ‘ -•- •' yu 

^ .vj-. •> , v .>;; 

A » rfV^fr/Vi ° 'O \V * 

. AWA° 

^. 'f ^ : p®« **> , ^3n 


x \ v ^ - 

/ V V • 





«, «$> 



*■ *f> 

* -v. 


,* v"^, ’W 

A C ,C> o ■-. 

if . •. ^ ,o .• A.V-. o 0 


' A*' ^ ° - "*^v 

y> K O ^ \A\J • ^ i ♦ ^ 

•• .«* °^. *•*•' a 0 *'■» *•■' 

v »**•% c- ,o ,•••» ; ji 

/ :» \/ ;1 

,j* o Y//^«\\V vV a t. ■> .r 

j .V J<^v'. <£/ ^Cw • 


o 'o.»* A 

. . ^ c * - « «, <S> 

A . < *P 

vp- A o - 'P/ A 




^ ^ \^m: ^ 

a * A 0 ^ ' ' ’ <? 

,o , • • \> v **;;% <a 

^ .»*V A. 

£ 1 e S ^ * ’WA'WSS • . V«* 

• -* e c"? -% o (///Vi^wvl' ^ - 

<. "^Vi‘ <0^ O -•■.;* 4. _ 

o « *^5‘ ry . ' * ♦ o 0 0 " 8 « ^ 

+ *& S^jT)9o.^ O .i^ • _c«tv «#* 


N *<» 

.v, ^ " * ' 1 ‘ < $ °<u * * " * A~ 

. V sY •*•••. > v % c> o v ^ 

^ *i(f\^ A < 'o & * ^l:v\ * ^ c.^ 



* </'> - 
* aV 

^ <?* 


vP, ° 

CV* • * 

O. '•. * * A .4 

* ■* ^C* c o “ « 4 

-» o *P 

0* <. <JsN\ , An'^ ~y 

^ O 

o V 



A ^ 


^ *-*.•• ,0 





,* / '%. *y£%' y s v 

G* o '<■..* A ^ . . , 

t> v .».«, *^ 0 , o * «* <p 

u i _ » o .A 



* 'X, 


<J.’ ^ 


'’o V 

, * ^Tyf A/ % a r 


.'” >0V ^ ‘.^ar. K 

’ ,°’ ^ •., . • A °^. *•'»•’ a 0 ' '<» '••’■ A' 

.0 . • •»- > V »'•■'. o O' .••<•- > v % v’A 

** .*^V/k* -VSUV- % A .‘A’. ^ -A .N 





*«<& 


y)W. : Y'% 



&*• 


^ . ■_. w- * <(,' &. >* "V 

- a <r ^ '. 

^ c °y ° * 4 » . *■ • • 4 "^o 


j^S’ • 4 O . 

PI' ^ ' 


* V ’ w 






a,, • > 


’% » ^ \^§!pr > s •»* u . * 

+o ••?..*’ A ^ ' •• ■ ‘ /' % ••• a> ..... V 

.... % A .•“*., ^ f 0' k'Jjy^. °o h* .\tf58W.. -v 



>y . 1> o 


# *y, 


£>* °v 





% ^ • ’ / 

v s s •:/./. «: 

^ ^‘ v .y^ 




**0« -cr« . 0 

° ^ ^ 

O' • " * °' ^ v fc 

*#> A^ * ^<?aT° ^ A^ * 1 

• +*«<* :MWh° \$ 

**> -»«?■ ^ \% 
; c?"jv ^’ ''<? V "• 

^ '•" o- .-.\ ,/.^W ‘ —^ 

^p ' V; t ,v>2-. -• O J aN\\\V*v ^ . 





^ r A. 

«T Co ' «'^«"’ .v. 

t) •> • A v <*► • ' ’ s . . , Cf 

> t - * /> C' O' - * * * °* ^ ^ '*-£> A^ 

v ^ ,V • a ^ a .*c «j> > • «»&• ^ <£ : 

❖ , v • ^ * 

^ ^ y ! * <• j-> * ^AV^'r^ * 

; a s % Mm?.- <? %■ ■ 

.’ *-f/N A <. 

'o -*.> A <>'*** w ,. / 0 °“*^ ^ 

A % ,0 t* ^ * °o j* • 



\P- A 

^ ^ * 'N^ a - J ^y - CvT 

o C^ <JV 

‘ * A y ^ . ^Taiilrri * &/ 

* V <tv *N^nwr» ^ 

>o *«?.?*‘ «►*'•••* * 6 .... 

... ^O ^ % C° .* 

■" ‘ ^,. « 


N. MANCHESTER 

i k i r\i A M A AfiQfi? 


^ * 4, ^ V * * * 

<> c* V ' 


































































































































































